Details Page for 0.3163

Complete Solution is Known:

MSV File: q-0.3163.msv

Growth Pattern:

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Details for Q₁₉₂₅(0.3163):

Q = <a,b,c,d,e,f,g | a²=1, b³=b, b²c=c, c²=b², b²d=d, d²=b², b²e=e, e²=b², b²f=f, f²=b², b²g=g, g²=b²>

P = {a, b²}

Phi = 1 a b b² b ab ab² ab b² c ac ab² b ab² ab ac b² b b² ab ac c b ab² b d b² ab ab² b d bc ab ab² b c abc ab ab² b d abc ab ab² b ab² abc ab b² bc ab² bd b d ac ab² bd b ad ab b² bc c ab² ab d b c ab² ab b² bd ac ab² b c bd c b² bc d ab² b bd abd d abd c b² ab ac bc c bc ab ac bd c abc ab ac bc ac ab² acd c b ac abc acd c bc ac bc cd ad abc c bd c ad abc ac bc cd ab² abc c b cd ad bd c bc ac d b c bc ab² bcd bd cd ab c bcd b² ab² abc c bcd bd bcd bc b² bc abc ac e c bcd ab² ac bc cd ab e be b c abc e d bd ac bc cd c e ac b cd be e ac b bd ab abd c b cd ad e b² bcd ac ab e acd abc cd be bd be ab b² abcd b² ab² b ab² b e ac ab abd ab e be abc c bcd ab² be bc b² ab abd be b d b e be e ac ab ae bc e acd abd ab² be abcd ac b e be ad ab² b e abc e cd bc b² be e be bcd ab² b e cd abcd b² bc e bd abc acd be c be ab b² ab ad acd ad c abc ab² be bcd cd ab ac be bcd bce b c abd ab ac bc ac bc e acd abd c abd d bce bc ac abd ac c bc c abc e bce bc ab² bc ce be abc c abc c be ace ac bd ce bce ae ab² abc c abc bc ac bc ac ab ce c abc ab² be e c ab ac bd e d abc ad b ce ac abd ac bd e d abc c abc ab² be bc c ab e d bc d abd ab² bcd bc cd ab cd be abc ab² abd ab² be abc ac ab ac be abc be bd acd abe e bcde bd ac abcd abc be bd ab² abe e be ab ab² abe e be abc acd abe ab² ac ace ac ab e ab ae c abd d be cde cd ab cd be bcd d ab ab² be e cd abcd acde be e ab² abc ab² be e be ab ab² ab ac abe bcd ab² bcd e be bd ab² ab e be bcd ab² abe d be ace ad ab d be ace acd ab e abe abcd abce bd ac be e d bcd acd abd ab ac ab ad abe e abce abc d bde ab bce ab ac bd e bce ab ab² abce e abce bd ad bd ac ab² bcd d abde ae bce ace ac ab ad be cd ab² abd d be ce ad abc ac bd ac d ab ab² abc e abce ab cd be e d abc ac abd ce bce ab ac bd cd d abc ad abd e bce bd ac bd e bce abd ab² f c abe bd cd bd ac bce abd d abc ab² bce bd d bd ad be e ac abc ce abc e ad bd ce abe e abcd cde d bcd acd ad bd ac abce ce be bd ac abd e be bd ac abcd e d ae ac abd acd be bd ac abcd e abcd abc d f cde be e cd bc cd abcd e c abd acd bcd e abe f ad d e bcde abc ab² be e bde f bf abcd e be bcd d abcd e be de cd abcd e be bcd acd abcd acd b e bde f cd abe e abe bcd bf be ae bce bd abde be e be bcd acd abe ab cd abcd ad abcd e bd f acd bcde e cd abcd ad d e abe abcd acd be ce be ade cd f af be bcd cd bcd d be ce cd abcd acde be bcd acd bcd f cd abcd cd abcd af abe e abce bcd d abd abcd abd bd abf abe ad acd bcd acd af d be abcd ad cf bcd bc ade acd abd e be ace ad bd ad be ce bcf bd d abe abcd cd bd ad be e bcf abd ad abd e bce bd ad bd e abce abd d abd d abce f ad bd ae bce cf d bd e be cde ad abd ad be cde d abd ace be e ac abd ae bd ce bf abd d be ab² ad bd ce abe abc d bd af abe e be bd ad abcd ae bce abd acd f e bce af ad abcd e bce abd bf f acd ac e bf bd ae abcd cde abf af acd ad e ac abcd bf be e abcde abd bf be bd bcde abcd bcf c abd be abc bf bcde ab² bcde f bf abcd e be f acd abcd e be acf cd abcd b² d ae bcf abd acd be ace cd abcd e abe ce acd f bd abe abcd abcde bcd bcf ab² ae bce bcd acd be e bce bd acde f e abe abcd acd be e ad abcd bcf be ce be ac cd acf e be e cd abcd ae be ce bf af ae abc d bdf abcd bcf bd ac bf abd d be e cd bd bcf abe ac abce bcd abcf abe abcd abce acf abdf bde ad be af d df ae be ace abf f b bd abd ad cf e abe ade bf df ce be cf bf af ace abc ace d f bdf abe ce abf af ab be ce ad f bcf bce ce ab f d abce ce ad bd ad abce ce bce abd abcf abce ae be af ad abce ac d bd d cf ace be bd ad df ce d ce d f abcf abe acd bf f ace be abd d af ace be bd be f abf abe cd d af bf be bc abe af bcf bce e be cde bf bce bc be acde abf df ae d abd abf df ae ac bd bf f ae d ae abf f acde be e ad f abc d ac abe af bcdf be ab² be af bcf abe e be f bf ac e be f bf f e d af bf adf e abe abcd bcf abcd e be ade bf af ae be f cd f ae bde acde bf af bf be ae abf af bdf be bcd abce ad e b² d abce f abf bcde ae abde af e acf abcd abc d cd abe ade bd bcd abf acdf e be d cd cf ce be ac bf af bcf abc ae abf be cde bc ce bde f abcf cd e bce acf bcf acd e bde af ab be d abce f ad acf bcd abce af bf bce d abc acf bcf acf ce acd cf bcf af abcd bce acf abf ab² ce be b² bf abd ace bce ace abf bd bcf be ace ab af de bce ce ad f bcdf bce ce ab bd abcf bce e bce af abf acd ce ef cf abcd af bc abcde ae abf cdf ce ab acde bf bce abcdf abe ab² d acf ade be b² bf af ade bde ab² bcde f bcf c b² bcde af bf be ae abcde f bf be e ab f bc abcde bd bcde f abf f ae bcde acf acd ac cde ad acde abf c e be acde bf cdf e ad e abc c abf be ac bf af acde abe e bcde af bcf abe acde abf f bf be bd be f abf bce cde abcde abcd bcf bcde bc abc f bf bcde ae abcde ac bc be ae bce abef bf abcde abd be ce bc abcde acde be c abc cf ae bce ac abde f e be ce abc f e bcde ce bce f bf abcde abcd bdf d abf abcde ace abde f bf acf ce abf f bf f b bce cf bf af abcf bce ade abf af abef abce cf bcf acf abcf bce bd abf acf ade ab² e abcf acf ab bce ce bdf ab² bcf bce ce bde f bcf b² abcd bce f bf ab² ad bce af bf af abcd be adf abf ab² ce bce af bf f abcd cd acf bf acf ce abce ade ab df ce abce bd bf cf bcd acd cde be cd abcd ef cde bcf adf abcf cdf de abe f bf bce e be acd bcf bce de ab af abf acf abcd bcde cde bcd acf abc bde cd abf af bcdf be cde bf af abd d e bf cf bd abe acd abf f bef c abc d cf bf ac bd bcf f abf d abd be af bcf ac bd bcd f abc acf e be af bf af e be ab² bf d abc d bef bf cf bd ac bcef bdf d abd d e bf ad bd ad e abf d abd c e bf df bd acdf cde abc f bf f abd ef acdf bd ad ae cef d bcf af abd cef abcef bd ad bd cef bcef bcf f bcd d acdf bf af cde aef ade bcf acf bcf be de bf af abcdf ad bcef bcf f bcf d bcef aef cf abcf cd de abce abcd bcf bcde cde abce f bcf cd bcef abde cf bcf acd ace cef bcef bf af ab abc bcef bcf cf bcf abce bcef abdf af ab b² abef bcf f bcd bde de bcf acf abcd cd ade bcf acf bcd acd de abcf cd abcd bce de ef acf bdf acd bcd ef cf bcf cd bd acef adf bcd cef abf be cf bcf cd abcd bde bcef bcd acd ade abde b² abcf cf bd ef e bcd acd bcf d e abcd f bcf cd bef abcf acd abdf d e be cf abcd cd bef bcd bdef abcdf acd abc be cd bcf ad bef be acf bcf cdf abd d af abf af bd ad ab² bcf cdf abc be bcef ef af abcd ad bcef bcf cdf bcdf cdf bcef bf abcef abd be e be d bcdf aef e abcde cf abcd ac bd abcde cdf bdf acf abef bcde ac bcdf ad ae ad cdf abcdf acdf abd cef cd bd cdf bd cef bef abcdf d bdef bcde acdf bf ad abdf aef bcef bf acf bcd d bcef ef ad abd aef bef bcd d bdf d cde cef cdf abcf def bef abcdf cdf bf aef bef cef bef abdf cd abef cef cdf abd acd abd acd bdef bd ad bdf cef d abd g abd cef bcef cef ad bd cd bcef cef f abd ab² ace cef ad abdf ad abcd ef d abd acd bef abdf df abcd def abcd ef abcef bdf d bdef aef abcef abcd ad abef abde bcef abd d abcef cef bef abcd df abdf aef bef bdf df abcef ef bef bd abcdef abdf ef bef bdf g abd cef bcef cdef ad abcd cef bcef adef adf abcf acd bef cef cd bdf cd bef def d bcd acd bef cef cd bcd ad bef ef e bdf def abc aef e abdf adf abcd acef abef bcd df abcdf ef ae cdef ad abcd ad bef bcd d abcdf ef bef abdf adf bcdf ef bc acef d bcdf cdf e be g abcd cdf e acef acd abd acd bef be abcef bcd cd abdf ad cdf bcd d abd aef e bd cdf bcdf ef bef abcdf d bcd be abcef cdef cdf bcdf be bcef acef d bcdf adf bcef bd g abcf cef bef bcd abef abd acdef bef cef bcdef abcd d e aef g abd g e cef acdf bd cd ag ef bcef bcd d abcdf ef bcef abdf ad g ef bcef bcd cdf bcd ef abef bd ad abcd ef bdef abd d bcd ef bcef abce cd bd aef bcef ef abcef abcdf acdf abef bc ad abcd abg abcd cef d cg acg bcef be acdf bd cd g ef d bcd adf abcef cef bcef acef cg g adef ace abd adf abcdf ef bcef bd cd abdf adef bef bcd adf abcdf cef bef ef ad g abg bcef cef dg cdef acd abcef cef ad abcd cd abcd ef d abd acd abcef ef abdef bd ae abe ef bcef bcd adg bcd ab² abdef abcd cd ade acef bcdef abd acd de ef bcef ef ad g cef bef ef cg dg adf bef ef cd bcd acdf bcef cdef acd abcdf cef bef cef cd abdf ag abcef ef acd abd acdf abcef acdef bdef bd cg acg aef acd bcd adf abd acdef bef cef acd abg ef bc bcd g cg abdg bef cef cd bg g abcdef ef acd bcd acdef bef ef cd abcdf cd bef b d dg acdf bef c cd bg bdg adg cf acd abd acd abcef d abdef bcdf ag abcdef ef abcef def abcg acdg aef bef def ag dg cef bef bcd g acde aef bef cef ad acde aef e def acd acdg aef abef cef ad abcd ag e cf bcef bcd g bef ef bef cde ag abcg ef cdf abd eg bdef ef bef adef cdf f ef bcef abg abcde abg aef bcef abcd cg abcg def bef acef acd abg dg bef cef d abcd acef abef abd dg abg adg bef ef ad abcg cg abef ef d bcd adg abdef aef bef abcd ag bdg ef d bd adg bcg ae ad abcg ad abdg ag d ef acd bcg aef bcef bd ag abdg eg bef ef acd abg g bef bd adg abdg dg bef cef abcdef bcd acg bef adef cd bg ag bef ef acd abd g abef aef bef cdef cg ce ef bef bcd g abeg ef bef cef ag abcg acef abef bcd d abg def bef abcd acd beg acdg bcef bcd acd abg ef abef aef bcdef bg cdef abef acef bcdef abg acg abg acef ad abdg ag abef ef bcef abg g bg aef cd abdg aeg bcdg aef bc bg g bcg aef bcdef abcd ag adg ef acd bcd d abg aef bef cef ag bg acdg bef acef acd abcdg g abdef cef ag bg eg bdef bcd d bg acdef abeg cef bcef abcd cg abef abe adeg abg acg abcef ef bcf def ag beg acef d abd g bcg acef cd acef abcde bg def bcef bcd abcde bcg acg abef abcd cd cde acef abcdef cef bcef abg bg ae abcd ag beg cg abcdef cef bcef bcg cdg af bce bcef abcd eg bdef acef abcef bcd adg bdg cef ad def dg abcg aef bcef bcd g bcg acef bef cde bcde bg adef bcef abd cg bcg def b adef g bcg acef abcef cde cg bceg acg abcef cef cd abcg acdg abef acef bef bcg acg bceg bc cd abcg cg bcef acef d bcd acg bdg cef ac acdef cg abcg ag c bdg bf aeg acde bef acdef ag bg bce bef abd acg bceg acg bcef aef cd bg ceg bdef ef abef bcg eg bcdef aef abef f acdg bg abc bef bdg acg abcdg aef cd ade acdg bg aef bef af cdg abcdg cdg abcdef aef cg bcdg ef e aef d abg cdg bcdef cdef cg ce acdef abef acef bdef abcdg eg bef f bde bg acdg abcdef bcf abcdef bdg g bef aef bef bcdg ag bg aef abef abg g bcg aef ad ace ag bd ef bcef abcdg cdg abg aef abc fg acg bg cef ab² ef g bg eg b² acdef cg bg bcf bdef aef d abeg g bef cef bcf bcdg ag bef bcd bdef abg abdf abcef aef bdf abcg abe abcg be cdg acef g bef ef abcef bcdg g abcg bcd abcef cf eg abcdg abdf abdef adef bceg bg aeg ab² cf adg ae abdf acdf bd dg bg abe bcef aeg acd abg acg bdef aef bcef abcg cg abdef cef bcef abg aceg abg adef bcef abcg ag bg abcdf d abg cdg bcg bf bef abcd dg adf abcdf bcef cde adg bcg bf ac cef dg abcg abcdf d abd acg abg acg ac bc adg abcg adef abcde abc adg bdg acg acdf cef ag abdg cg bcef abc d bdg g abg cef abcef abdg dg bcde abc bcef af adg abdef bd ad abdg ag abdg cg bcef acdef bcdf acdf g ac f dg abcg abcdf c abd adg bcg cde abcdg bd bcdef abdg ag bcdg abc d abg g abcdef bd bef abdg abd bg acdg bef abdeg g ce bd abef f cg bg bcf abef bcg acg abg acdef b² def acdg adf bdf abeg acef adg bdeg abcf bcdef ef ag abdg g abcdef fg cdg bcg g cf aef acdg bg ag f b bdef cf acg acdf ab abcef abcg ag adf bdf bc abcdg g df acdef ac acg cg adf bcd bcdef bdg abdf df be b² acdef cg abcg bdf ab² abcdg cdg abg cdg e bd bcef bg bdf acd fg bcef acef abdf af cef acdg acf cg f def bfg cf cdg df def abcef bcdg dg adf def abcef df adg df abcd abcde def acdg bcg cg bcef fg abcf e bcdf abeg fg dg bg bdf acd acef adg acdf bf bdef bc dg bcdg bdf abcdef abc cdg fg abdf af acef bfg abdg abf adf abc bfg df g af bd acdg abcg abcdf f abcdf bfg bdg abcd df cef bfg bcdg deg cdf abf d fg adg df abdf ad abdg bfg cdf abf d abcdg acg bcg bf ac adeg dg abdg dg d bdg adg bcg bcdf ce bc bcd abdg abcdf c abd bcdeg bcg acg abcde bc dg abdg abf adf abc abceg af adg df bd ac abdg abf cdf abf c fg bf acdf abdf bcdeg bcdg dg df bdf d fg bf bcg abdf ac bd dg adf bdf bcdg aeg acg bcg bdf ad bd abcdeg bcdg acdg cf bcd abef df cdg df abdf bfg f cg adf bdf bef df bcfg df abcf bef abdg abdf adf bdf bcdef bdg abdf bcg abcf cd bd bdf bg bcf adf afg cdg df abcf df acdef bcg adf abcdf adf bcd cdg cf bd cd abcd bfg bcdg bcf acf bcf bfg abg bd df ab acdg abdg bdf cf bcf ab² cg bcdf adf abdf ac bcdg acdg adf bcd acd abcdg bdf df abcd b² bcdg bdf df bdf ab² adeg bfg cf abcd acdf ceg abcef acf bcf acd deg adg df abcd af abcd b² adf bcf f abc ab² bdg abcd df bd ac aceg bdf f abf cdg ceg abcd df bf bcg fg bcf acd abf abdg abcdg abdf cd bf acdf aceg dg acd bdf acd fg adg cd abcd cf bd abceg f bcdf f b bg af bf acdf bd bceg cdf abcdf f abd cdg cd acg f bd ac abcg bdf cdf abcdf c bdg bf af bc ad abdg abf f bcf c fg bf af bf ad bd bfg bdg abf bg cfg bf af abcf ad bc bfg cdf bf f ag adg af bd ad bd acdg cfg abf f abc ab² bdg bf ad bd abcdg f abf adf abc ab² cdeg abdf ad abdf bcdeg abdg abf d abd d acdeg bf ad bf df acdeg beg d bcf acf abc bfg af bf cf ab bfg f abd ab² abc abdeg af bf af aeg abeg cdf bcf acf bcd abcg abcdg bd cf bd cd fg bcf cf bcf abcg cg abcf df abcf cf fg bceg f abd acd cg bcdf cf bcf cf bcdg acdg f bcf ab² fg adg cf abdf cd ab acdg df bcf acf bcd adg ceg bf acd abcf acdg acf bcf acf bcd cdg df bf cf bd cd fg abcf f bcd ab² abcdg abcd cf abcd bcg aceg abceg acd bcd bdeg b abdf cd abcd cf ceg bfg adf bcd ab² abc bfg ceg abcf af bcdf bdf acf bcf adf bcd bfg df bf cf bf bcg acf bdf f abcdf d bdg bf af bf abceg aceg bdf cdf abf cdf abcdg bcdf af bf af abdg abcdf acf bf f abc adg df bf af bd ac f bcd f aceg adg df bf af bf ac adf abf f abd adg cd bf f bf ad afg abf cdf abf adg fg bf cd bd abcdg abdg abf d bf efg abc bcdeg f bd bceg abdg b² f b² abeg dfg bcdf af bd abcdeg cdeg b² ab abd f eg bcdf ad abcf d g abg f bcf af eg beg acdf cde af abcf abdfg ab bdf f bcf abeg b abdf af bf abg ab abf f bcf acf b abfg cf bf df eg b² f abf acd bcg bcdeg abcde bf cf abcg b² acf abf f acdeg ab² b abcf cf eg acdg acf abf f bcf cdg b bf df abcd b² adeg bdf f ac ab² ad abcf cf abcf abg ab dg abde bcf beg abcdg abdf cf bf bcdeg acdeg bdf acf bcf acf dg cdg cf c af deg ac f abf acf deg abcg cf bcd abc abcd acdg adf bcf acd abf abceg abc bf af bf ac ab bcf f abf bceg df c cf abcf bdg acd bcd f abf f dg c af abcf af adg ac bc bcf f abd abcf af bf af aceg bceg f bf f abd cdg fg bf af bcdf beg ab ce f abcdf abceg fg bf af bf acdf aceg abf f abf abcg abd bf f abcf bdeg eg abcdf f abf bdeg aeg abcdeg bce abf abdeg ceg abeg f abf acd befg abceg bde bf af ceg beg ab abf cdf aeg adg abe bf df abcf abeg ab ae f abf bceg fg ab² af bf bdeg abdg acde bcde bcf beg acdeg ab² b bf abeg bc abf be bcf acf aeg abeg be bf fg eg bcdeg ab abf afg bcf d abcde e af abcg abeg ab abf acf ag acg af ae cf abcf beg cdeg bcf f bdf beg aeg e cf abcf abg afg bcf bcde bcf beg cdfg ab² bcde abcf abg f bfg abe bcf acf deg c cf bcf df eg bfg f bcf acf bdg bceg df abcf cf cdeg abd bcde ae f bcg efg df e af acdeg bdg afg bfg f cdeg beg b ace af bf bcdeg cdeg bcf f bcf cdg ceg e bce bf bdeg eg bdf abce abf cdg bcdef d abe bcf abcdeg eg b² bce ce bd deg abdf bce ce cf bcdf cdef acf ace f abg abdg bde ade af bf bceg abe abf f abcdf abceg aceg d af bf abdeg cfg abceg f bcf acdef ceg aef bce bf af adg ac abce bf f befg abcd bce bf af ceg bcd f bcf f ceg abceg abc bf af aceg ac cdf de f cd abcg bce ace f abcdef bcd bc ad f abf g aceg bf abe bf cefg cdeg ce be abf g ceg d af bf ag eg ac abde bf f deg beg b bf cf aeg abcdg ab abf acf ceg def abe cde af abcf afg cdf ae f bcf def abcef ae cf abfg abeg abdg ae f bcf acf eg ab² abe bf abeg abde e be abf acg bcg bcdf bcd abdg abeg bdef ae be cd cf abdef adg abe cde cf eg ae bcef ae acf abdef cef abe e cf bdef bcdeg abcd cd acf bcg def abcdefg e af abcf beg aceg e adf bcf bd abcef e abe bf adef abfg ae abe abf bd bcef def abcde bf abd c bfg be abf f bcef cef be d cf bf abceg be ae acg ac abeg abe e cf d acef abde abf bd abcdg bc bcdef ce bcd d abd bdef ce bd abf bcdeg abcef c abd d acfg bcdef ae abde bcf bcdeg abcef ace abd bf cg abcdef aef bd abf bd ad def abe d abd ceg bceg bd de bd bcdef aef abef d af bg cdef bcdef ce f ad cdef bef d abd d acdef abce ace bd ad bceg bcdef c bcd bf cdef aceg ad bd abf efg bcdef ef abce d cdef bg ace bd abf f bcdef abceg abcde bf acdg acd aef cdf bcf g bef abceg bce e af acd ag abcef cd bd cd aef acdeg ade af acd abcdeg aeg e bd cd f abdef ace abe acd bcd abefg e abcd cd afg abdefg cef bcd acd bcd cdeg acde abe cd abcd cd acef abcde e cg abfg abeg f cd bd ad adef abe e bcd abdg acef bcef e abcd ad acg af acd abe acd abeg abcef ae abcd cd abeg abcef cef be acd dg bdef abf be ad abcd bdef cef bcd ace abd bdef ef abe cd acg ad bf bef acd bcd bdef abc abe abcdg f bcg bc abe acd b d adef abcef acde bd ad afg abdef d abd d abd abef ae adfg bcg bd bdef aef abe acd abd bcdg ef f bdfg bd abdef aef abef e abd abdef ef bd abcdg bd abcef g bef d abe bg acef f adef bd ad bceg cf d adfg abcg acef acf ef bd ac bd abcdef ef abe d abc acf ae adfg abg g bcdef ef abce abdg ag aceg ef bd cd abcd bef ef abd acd abd bg aef f bdfg g cd ef cf d bcd bg acef be ce adefg cd abcd bef d bcd acd bcd bcdef bcf bd ad abcd deg e adfg bg abd abcdef ef abcd ad bd b² ace cf d ag abef ef acf cd bd cd ace abcef bcdg bcd acd ef bef abcdg g b² aef acdf bf

Monoid Structure