Details Page for 0.3146

Complete Solution is Known:

MSV File: q-0.3146.msv

Growth Pattern:

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Details for Q₁₃₅₁(0.3146):

Q = <a,b,c,d,e,f,g,h | a²=1, b³=b, b²c=c, c²=b², b²d=d, d²=b², b²e=e, e²=b², b²f=f, f²=b², b²g=g, g²=b², b²h=h, h²=b²>

P = {a, b²}

Phi = 1 a b b² ab² b a b ab ab² b c ac c ac bc abc d ad b ab² ab b ab² b ab² cd b ac abc c ac bc ac d ad d ab² b abd ab² b cd b cd ac bc cd c bc ac bc abc d b d b ab e b cd acd cd bc abcd abc bc ac d abd c b bd b ab e b cd abcd cd acd bcd bc abc e abe abd d ad d abe ab e abe b bcd cd acd cd bce abc abe ac ad d ad d bd e de abe e acd cd acd cd abcd ace de e ad ac d ad bd abe de e abe ab² cd bc cd acd bcde f abde abe b ab² d ad bc e f abc abe cd acd cd acd abcd b f de ad ab² d ad e bcf bde be abe ac bc cd acd abcd b f ade b d b d cf abe bcf ade abcde c ac cd ace b ce b ade ad ab² d ad cf f af acf c cd ac cd abe ab² b ab² ace ade ab² d ade adf ac be c ac cd acd f abcd ab² abcd b ab² bce ab² de ad acf abcf e c abc c bcde f abf af f cdf ab² ace ab² b abde ade acf c abc abe c bc cde f af f af b ab² bde b cf ef ade cf df bc c abc ac acde bcde b f af ab² ade de abcf abe cf acf cf ac abcd acde c ef acde af ab² f cdf de ade b ade acf abcd cf bcd bc acde c abe abdf af b e abe de ade abe acd bde bc bcd abcd cf bdf acde bdf abdf abf ab² bcde abd f abe bcdf abcd ade abcd acf cd abdf c bce acde ef bd abd b abe f e bcdf bcf abcf acef cef acd abcd c bdf acde bdf abdf bdef abe e abe e abcd abe bcdf bcef acf abcd c bcde ce ace abdf ef abdf acde e abe e abe abcdf bcdf cdf c abcd c ce ace abce bcde acf abdf abe abd e abe e abe abcdf bcd cd cdf cd ce abdf ce abdf abf b df e abd e ae abe e abcd cdf bcef cd ce ace abce abf bdf d df e abe e abe be e cd cdf acd acef bf ce bce ade df adf bdf aef abe ac e ae e cdf abcd bcef cde bce abcef acef bdef df bde ade abcf abd bd abe ae be abe abcde cd acde abcef abf af f bde de ade ad ef abcdef be abcf abcdf cde bcde abcd abcde bcde f af g ag bde de b de cf bg acf abcf bcde acde bcde abg acde f af f abf adef de ade cf bcdef bg acf bcf bcde bcdef bcde abce g f af f ade aef ade ef g abg bcdef ag cdef bcde acde cde acde abcg abg af f def bde ade de abe abcf bcdef g cdef bcde cde acde abcde acde bcde bdf f bf abe de ade de b g acef abce abdf c acde bcde cde bcde bdf af abdef abde de ade de ade g bcdef abcdef cd acde acf abdf acde bcde e abe abf f de ade abg ade bcef ac g abcf bce bcde cde df acg af abe g abf be g ade abcdf ade bcf ce acef cef cg abdf cde bdf bcdg abe d f g bg abe bcef acdf bdg ag bce ce ace abce abdf adf abdf abe e abdg abe ag b abcdf bcdf abcdf ce bcef abce abcg bce adf aef df abe e be e ade ag abcdf acef ce acdf abce ce bcg cg df aef adf bdf abe ae abe e g aeg abcdf ce abce acef bcef bf ce bdf adf df abe adf e adg aeg cdf acdf abcdf abcef abcdf acef af abce af bcg de df ef bdf be abe acdef cdef aeg abcdf acdf abcef ace ce f ace f de beg aef g abdf e abe acde abcdef acde bcdef bcdg cef acef bf cdg f af abdf bdg abg dg be abe be acf dg acde abceg cde abce af f abdef acdg de deg dg g abe g d abcf acdef acg bceg bcg acg af bf f abf de eg abdef g abg dg abcdef acdef cf acf eg bceg acg abceg af f bf ade abdef ade abde g bdg cef cf acde cf acde bcg cg abcdeg abceg def f af ade abe g abg ad acdef abcdef abcde abcf bcde acde cg bcd af abceg bde abf ade de g acef abcdf abdg abcdef acde abcde cde acde cg bcg cdg be acdeg ade de ade de ag d acef deg cdf acde acdef cg cde adf abe abc fg bfg g ade de acfg bg abcef acdf abdfg abcdg bcg cde acde adf abe e be abdg af bf de ade abcdf bcdf acdf bcef bcg acde acdg acde ceg abe e abe bdf afg adg ag adg abcdf ace abce cf abce cdg bcg acdg ef e abe bdf abe bdg g ag adg abcef cdf b bce abcdef bcg acg bceg abcdeg abdf abe e df g ag abg adg cef cdf acdf bcdf bce cdg acg cg e ef e abe adf g abg adg aeg bcdfg ace d ce cdf bcg acg cdg bcdeg aef adf abe bdf bg g ag abcdef aeg abcdf ce ace abce cdf bcg def ac adef ef adf bdf ef ag abcf cfg acf bcf abcdf abce cef abcdf ade bcg aceg adfg adf be abe ag dg abcdef bcde acf abce cdf bce acg cef acg f af adf adef bdf bg abdg abg acdef abcde acde acf abdeg abcdg bcdfg acg bcg ade de ade abe af bg abg dg abg bcde bcdef acf aefg bcdg acdg bcdg acg ade bde f af def abg g ag abdg acdef abcf acdg acde acfg acdg bcdg ceg ade abde abfg f af befg g bg eg bcdef acde acf bcf cf cg abcdg ceg abceg ade de f af abg g abdg acde bcde acde cde cf acde bcg be acdg ef ceg de af bf bde dg adg bcfg abcdf cde cf bcf cdef acfg bcg ef acdeg ade bf ade bde af bdg adg bdg ace acdef acde cf acde cg be e abdf abdef f af fg aeg ce abcdf dg cef cdf befg acf cdg e cdg abe bef bdefg bdf f abde bg bdg ace abce cef bce cdf cdg bcfg cdg ae abe abdf be af df adf dg abcefg abcdf bce abce bce cdfg cdf bcg acdg abe ae be f af df af adg abdeg abce cdf ce abcdf cfg bcdfg bcg abcg be ae be df adf df abfg adg bdeg adefg abdefg bce cdf de bcdf abcdf aceg bcdg e be e adf ef ag bg ag befg acdef ace cdf abcf acdf bcg acdg abe acdeg e abe adf bdf adf bg dg deg adeg acf cdf bcdf cdf abde cdg cg af abe bdf ef df adf g abcde abce ace ce cf bcdf abcdf bde cg abde ade af abf af abdf abg bcde abcde cde bcde bcf acf cf cfg abcdeg abde bcg abcdeg f ade af abdf acde abcde cde bcde acdfg cf acf bcdf acfg abcg bde de bf ade f bdf ag acde g acde bcde abcde acf bcf abcefg 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abcfg acef abde abcg abde acdeg af abf efg aefg efg acde aeg h bcf cf acf cf abceg abcdfg de abde de f af f af eg bdg cde acde acf bcf acf bcfg ceg cg bcg ade cdeg bf af bf aeg dg beg abdg cde bcde acde cf acf acefg ceg abe bcdg bcg f bce af efg beg acde eg adg bcde cf acf bcf abceg acg bcg de h ade f af g eg acde cdf adg abcdfg bcde bcf cf be acg abe h ade bde bf f af abce bdg deg cdf cde cfg bcf cf cdeg be bdf abd ade adf ade abf adeg g acde abdg acde cde bcdfg acdefg cdfg bcdeg acg abceg abe bdf adf af fg ce bdfg bce h acdf cdf bcfg acf cfg acdefg bcdeg abcefg h df f adfg bfg deg ag abdefg h abcdf acdf bcdf cfg cdeg acg adf e df adf bdf abdfg deg ag bg dg bcdf acdf cdf abcdf acfg abcdeg ceg bcdeg acdeg h adf h fg adfg bdeg ag bcde abh abcdf h bcdf acfg cdeg acg bcg adf df adf df bdf abdfg abc defg ag abcdf h abch cdf abcdefg abcdfg abe acg abh bdf df abdf df abdfg abdeg abg bdefg abcdf abg acdf cdf acdeg cdfg bcdg cdeg abe adf h adf dfg abcde bdg abh ch cf cdf abcdf abcdfg bcdfg acg bceg h abh bcdh df ch efg dfg bdfg adeg acf h acdh cdf ade abceg abcdfg abceg bcdefg abh bf adf bdfg aeg bdfg acde eh abh ag abcf bcefg cdfg bcdg bcdfg bcdeg h f af adh efg beg adfg acde bcde cf abh bcf cefg cfg cdfg abcdg abch f bf af b bdfg abdfg dg aeg abcde bcf bcdh abh cfg ceg aceg bcdfg abe af abf af befg h fg aeg abh eh bcf cf aeh acf ceg acdfg dh h ceh bde bf af fg efg beg efg h abcdf cf abcfg bc abcf bcfg cefg abch af bf bde f ag fg abdfg abefg eh dg cf cefg bc cf abceg abe aceh f bf bde f fg ag abce aefg acde abcde abdh bc acf abe c be abdeh abh f abdh af bfg bdfg aeh aefg bcde abch beh acfg bc cfg abceg h bcefg ceh de f abfg aefg fg abfg aeh eh bcdf abcdf abdeh acdeg cdeg bcdg bcfg acefg df f abch abfg bdeg dg aeg adh bcdf abcdf afh acf cdeg cfg cdeg acdeg h df abcdeh abdefg adeg afg aefg fg h bfh bcdf cdf cdfg acfg cdeg bcdefg ade h abdf bcdh aceh bcfh abfg bdeg beh deh bcdf abcdf aeh bdh dfh acfg cdefg ade bdf bcg bdf adfg abdefg adeg abfg acde beh bcdf afh abcdf acdfg cdeg cfg bde ade abe bdf abceh df bdf bdefg bfg abdefg abg h bcdf adh cdfg acdfg bcg abcdeg acdefg ade abdf ef dfg bdf abdfg fg adefg adh h bdh abcdf cdfg abcdfg bcg bcdefg ceh abde abdf acfh bdfg aeg bcde abfg adefg h acdh beh h cdfg abcdf cdfg acdefg adh ach abdf abcdeh cfh abcde fg abdfg bcde h aeh abcdf h acdfg cdg bceg ade abcdefg aceh abcdeh beh bdfg ag dfg abcf abh h bh h adeh abcdfg acdeg bceg bcdfg aceh af cdeh acdh bdfg fg adg bdfg h bcfh dfh abdeh befh h bcefg abcdfg cdfg bceh bcfh af defg bdfg abce dfg adfg h aeh abdeh acfg adefh aefh acdfg de abde cdeh abcdeh afh fg f dg dfg bdfg aeh bcfh aeh acf h aceg cdfg abcdfg abefh aceh bcfh f fg bfg bdfg aefg afh abefh acf bcdh h abe cfg abcfg bdh bceh acdh bceh f ab² cd adg acdfh acde befg beh h acf bcf bcg abcfg abcefg bceh af f fg abch acdf fg befg acdefh aeh defh abdfh bcfg cfg abcdg abcdeh acdeh aceh bcfh abcdfh cdh bg dg aeg bcdf h aeh abdh aeh bdfh acdeg cf acfg abef bdf acdh bcdh befh bg g fg bfg abfg aeh abh abcefh bdh cfg bcg cfg abdf abcdeh acdh abch bcdfh g abfg afg efh abh aeh adh abdh h bcfg abcg acfg abefh bcdh agh bcfh abg g bfg afg bfg fg aeh agh bdh h abcg acfg abcfg dfh abefh bcdh cdh dfg g fg acgh fg efh adh bgh h bcfg abcfg cg d abcdfh bcdh bcfh bgh adf g ag abdeh defg abh bdh cdfg adh bcgh acg b bcfg acdefg abcdfh ef acdh bdf abdfg acde aeh defg h aefh bceg acdfg cdg bcg cdeh abdef bcgh bdg bcdh abeg d aefg bdefg abe bdh ah bcf h cdfg acdg cdfg acdfg cdefg agh dfh abch ef bdg acde e abgh abh ah h abh cdg acdf acdfg bcdfg cdeh abdf bcfh ch bdfg dg abcde bdfg adfg efh h ah h cdg abceg cdfg bgh bcfh bceh bch abch adfg dg bdg abfg agh bcdef h adh h bcdfg cdfg bcdfg abcefg agh abch bcdh f ch adg abdg bdfg befg bgh bcdef abh bcfg cdfg acdfg cdfg acdfg abdef abch cdfh abch abg adg adfg c dfg abefh abdh abcdgh bdh abh cdg acdg ad bcfh bcdh ch bcdh aeg adg bgh bdh bgh adh h abh bcg bcfg acdg cdfg agh bcdh cdfh acdh ch af adg adfg agh bdh abc cg acf abe acg aceg bcdgh bcdh cefh bceh bcdh bdg fg afg adfg befg abefg bdh egh bcfg abcg cg cfg abcgh agh aceh abch abf abg defg bg afg aefg aeh dh h adh bcg cg cdeg bcgh abcgh cdh bcfh ch g abg bg defg agh adh abdh ah h cg acfg aceg bcdefg adgh acdh abcdefh ch g abeg abg egh bdefg dfh dh h adh bcdeg abcg bcfg dgh ch abch ch abdf fg ag afg bgh adh abh bcef dh bcdg cdf acfg acdefg ch abch abdf ach bdgh ag be ag bfg h abh aeh bcdf cef acdeg bcg acfg abcdefg abcdfh ach ch abch adg bg abg abfg adh abh h de egh bcg b egh ch bdg abcefh abeg f g abeg afg be egh adegh abcdfg acdfg cdg acg abegh bcfg abcfg cegh ach dg abcde dg g abfg bfg abdh h ah h bcdg abcdg cdgh abcdegh ch acdh ch bch bdfg ag aeg ac dgh bdh h bcdg cdg bcdg cdeg bcdfg abcdh acdh abch bcfh dg abdg aeg beg abcegh abdh bdh abegh abcdg bdfgh abceg ceg abce cdegh abch aceh acdh adg abg dg dfg acfgh bdh h adh cdg acdg cdg abcdg bcdh bcdfg bch ace ch bdg abg dg abdfg adh cfgh abh abe bcdg abcdg acdg abceg acdg cdh bch bcdh ch acfh dg bdg dfg bdh adh bdh h abe cg bcdg abcdeg acdh cdh ch abch abcdh abdg acef bg bdg cfgh bdh adh bdh be cdg acdg bcdg bcdfh bcdh abch ch adefg adg abdg acfgh acd adfg dh abh adh cdeg abcg bcdeg cde abdgh bcdh abch abg bfg bg deg eg cd bdg adh bdh adh abcdg cg ceg ad bcf ch bcf abcdh bfg ag ade defg befg adfg adh af abcg acg bcdg acde bcdef afgh bch cdh ch fg ag bg beg adefg aefh bdh adefh cg cdg cg acg abcf ch ach cdh aceh abcdfgh abg bg ag agh abh h dh acg cg acdeg acfg abcg bdfgh bch bfgh ch abfgh fg ag dfh abdefg abf abde ah befh cg ade bcg ch abch bcdh bg aeg ag abg abfg abdeg bdefg cdfgh f abh bcg ade egh cg acegh bcdfh ach ch g ef ag g bcegh abcdgh abh h abcdg aceg bcg cdg acfg abch ch abch ch eg ae g abg ac abfg ah bh aceg de bcg de ade ach abch ch ach dg abe g abdf abfg bdefh bh adh cdg bf af b ace acdh cdh acdh bdg g dg aeg be adf bdf adh acdg abh cdg acg ceg ace cdh cefh ace ch dg abdg e eg abcdgh bdefh bdf aefh beh bcdg abcdg ceg cdh cdefh ch bch bcdh bg bdg beg acfgh abdh bf h cdg aceg acdg cdg abceg bcdf abcdh acefh bcdf abce bg adg abdg eg abe bdh abdf abcdg adefh acdg bceg ceg bcf acefg ch acdf g bdg abdg adg adfgh bdh h be adh cdg acdg aef ceg acdfh ch ach ch abce g adg abdg abcdfgh befh abh abe adf ae cdg bcdg acdh cdh acdh abcefh dg bdg adeg abdg ade bdh befh abdh abh abdf cg acdg abcdg cf bcf bcdh acefh deg g dg abdg af abfh abh adh dh bcg cg acdeg bcde agh ch cefh ch bdg ag dg abdg ade abfh f befh defh acg cg acdeg bcdeg cde bcdefh bcdh cdeh bcdh g ag deg de adh de abf abefh acg cdg acg cf abcefh abcf cde abcdh fg bdeg ag deg abdeg bde adh abdgh f acg ceg cdeg cf acdefh bch abcf

Monoid Structure