Details Page for 0.3374

Complete Solution is Known:

MSV File: q-0.3374.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₅₂₈(0.3374):

Q = <a,b,c,d,e,f,g,h,i | a²=1, b³=b, b²c=c, c²=b², bd=ab, cd=ac, d²=b², b²e=e, de=ae, e²=b², b²f=f, df=af, f²=b², b²g=g, dg=ag, g²=b², b²h=h, dh=ah, h²=b², b²i=i, di=ai, i²=b²>

P = {a, b²}

Phi = 1 a b ab 1 a b c ab ac d c ab ac bc ab² c ab b e abc ae ac b abc c ae ac e ab ae ab² ac ab c ae ac e c b ab² e ace bce b ce e ace ae ac e ab ace b ce ab ace b ac c ab ace b ce ab ace b ce f ab ace b ce c ae b e f ae af b f abf af b e abc ae bf e abc ae bf b abf ab ae b e abc ae abce e abc ace af ce abe abc be bc e abc ace bc ce f ace af ce ab f be b abe ab ae b ce abf ace bce abce f abf ace bf e f ae bf e cf f acf ce abf f ae af e abf ae af e cf ace bcf ef f cf be bf e f ae be ce abcf ace be ce abf f ae af abe f ace bcf ce abef ace ab cef ce f be bf e abf be ab abce b abcf c bf ac b ae af e cf be c acf ac ace ae bcf e bc ae abc e bc ace abc acf abe bce ace abc ef bc bce be ef f bce aef cef ce f ae bf ef abf bef acf ef cf f acf af abcef abf acef acf abef cf abf acf bf e cf bef acf abe cf bef g abef ag ace be ce bc cf abc g acf ac aef g ef ag bef aef cef acg ag bce g e ag bce ae e acg aef bef abg abef bg bef abg e bg acef cg abcef acg bcef cg abcg ef ag aef g abe bc bcef cg ce e acg be cg acf bg cf abc acf ag bef abg cef acg bcg abeg g ef ag aef g abef ag acef abeg abcef af bg f abg beg ag acef abg ef bcg bcef f abcg e ag aef g ef ag aef g abcef bcg bcef cf cg acf acg ace g abef acf abeg cf aeg acf bcg abf g cef ag bef cf abef acf bef f abef af acg f g abef ag bef f e af ag ae g bcf bcef bef abf abcef acg aef f abcef bf bcef f cg bcf bcef eg f bcf bf bcef f abcef af acg be cg bcf bc eg f aeg af ag be g acf ag cf bceg acf afg cf fg g bf acg ae beg e ace cf cg bcf afg eg abcf cg b acg abcf cg abe abeg abc ce abe ac acg f e af abeg f beg bc afg abeg f abcg acf bcg f bcef af ae cf bcef e afg cf f g af ae ab bceg acf abcef abcf abf acf afg ace abf abcg b eg ab aeg ac afg abc abfg bc acf acg cf aeg bc ae abc beg bc bfg abc cf cg bc ae abc abcg ac abeg acg abcfg cg abcef f cf bcef ac abeg c aefg bc bfg ab abfg e bfg acg ab aeg af eg abc aeg bc abef abc f abg abef cf abc g bc efg cf aefg acf acfg cf cfg cg acfg acg abf abcg acf cef cf abcfg acf abcef bcg cf abcg acf abeg cf aefg cg abefg ab bcef cg bfg abceg bcg aefg acf acg f abcfg beg bcfg acg abcfg abcg bcfg bg h abg ah afg h aefg cg cef abc bcef abg ce bcfg h bcef ce eg h abfg abcg ce bcg ace g ce abcef h ace ah efg eg aefg beg bcfg abeg h g e acg abeg abfg beg bcfg abh ae abcfg ah acfg acef cfg af abcef f befg af abefg abceg acefg g abce cef ace fg bceg afg abh ae h ah abc abch fg ce bcg abceg ace bch ce abeg aeh bch bceg abeg be abfg bh acfg abch cfg ah ce abeg h abfg ah eg acef fg ah acfg ch beh bch eh eg ace aeg cef bfg bce fg abcef acfg ch acefg abcfg abeh afg ae fg bh afg bce bcef ach eh bcfg bcef aeg bh afg aef fg abce bfg abch bcef bch eh acfg bef abfg ce afg bef fg ah bcfg abch acef bfh abcef abeg ace fg abeh abeg ch cg bh abef bcfg bcef bceg ach abeg ace beg abcef afg bef fg bh bcfg aef bcef aeg ce eg bcef fg abe eg aef abfg abcfg bh afg bcef fg eh afg bcef fg bch bcfg abch abcfg aefg abef abeg efg fg cef afg abch abcfg bch abeh abcefg h aefg abcef afg aef fg abcef abceg bcef ch acefg abeg fh ch abfg abcef bfg abh abcfg cef acf bceh abch abcfg ach cefg h abfg abcef bfg ch abf abcef abeg efg abh cfg eg ae bcef aeg abeh eg bcef aeg aefg eg acef h aefg abcef abeg h f ah af cefg h abcfg bch bcef abch abfg ah ag abh h abcef acg bceh h abcef ach bcfg abh cf ach ag ch abh befg ah ace abh bceg ach bfg ch cf af ach abfh abch acefg ach cefg ch abcg acfh bg beh beg ah abeg abfh ch bcefg bch bcef aefh g e eg fh aceg bh bch bcef h fg abefh eg abh aeg efh abeg afg h abcfg acg bcfg abh beg bch abeg abh beg acfh abceh bef abh fg ah abeg h beg abeh ach bfg cg abfg acg bfg abh acfh ah abefg bcef befg efh abceg abcfh aceh abfg bh abcefg h aceg bh abceg befh bceg ach cefg ch abch fg ach abceg abh g bch ag ch aeg afh abeg afg ch beg ach abeg bcef beg ah ag h ch cfg abef abeg beh beg ah bcg h g afh abceg cfh aceh abfg ah abef h beg bh eg fh h afh bh ch beh bceg ah ceg ch g ach ag ch beg efh bh fh aeh beg eh ag aeh bcef afh bfg fh bceh abcefh ach abeg bceh g abceh ag cfh beg afh bch abfh beg abcefh bch eg h g ah eg fh gh afh ace abcfh bcefh ab² cefh acg abc g acfh abceg cfh bceg bcef ach acg abgh g bc ag aeh g bfh ceg cfh abc ac abeh bg abcfh g bfh abeg fh abfg afh bgh acgh cgh b bgh ag aceh aceg afh acg ag abch g cefg ab beh cg bfh acg ch bc aegh abceg abcfh bcefh cg abcefh acg cfh abg abcefh af abcfh g acfh abeh bgh acefh abg abeh ag abcfh g abefh abceh abfh aefg b abefh ag acefh g abeh ag befh cg abeh bcg abcef aefg g abefh ag aefh g abeh acg fh abcg afh acg bgh abfg g efh abc aeh g bef bcg af abcg abefh bgh agh aegh abg abefh acg aeh g afh bef agh g beg abefh ag acf g afh ag befh bcefg aegh agh bgh fh aceg abeh ag aeh g acfh bg beh ae abcefh bgh abcef fg g bcef ag cfh g bcef acg abeg af cf afg abceg abcfh ab efh ag bceh g eh cf abceg acefg cg eh ag fh abcg afh ag fh g abcefh cf abceg aefh aeg ceh bcg b g beg ag cfh fg g acg bcg abfh bceg ceh bc abch fg acfh bcfg bcgh abcfg abgh acfh abceg abfh cg bfh acg bcf acegh cefh bfg acefh abfg aeg acfh cf bceh abfg acfgh afg aeh abfg abgh afh bgh fh beg eh abeg h fg abf abcf bgh g abcef afh acg fh cg bch ag abch fg efgh bfg bcgh bf cgh afh eg ch aeg bh eg bceh bcefg abcgh abc agh aceh cg afh eg acf bceg ab acfg abcfh abfg begh abcf cefg abh aeg bh abeg bceh befg begh bcef beh abfg bcefg afg acf fg beg abgh afg beh aefg gh afg efg cfh abcg cf bcgh abch bceg cf bfg af cfgh gh bfg bceh abch aceg abeh abeg aceh abcef f cefg efg abfh f bcef acg fh aefg ach abceg ch abcfg cg afgh agh fh aeg bcfh eg af cfg bch efg ce acefg acegh bef abcefg fh bceg bfh efg fh aefg eh bcfg bgh bcefg bceg bfh acg abch abcfg afh bcfg beh aeg bcfh bcef h abfh bceg bfh acg abef bceg ach bfg cfh e bh abefg bgh cef bceg afh bfg ef beg aefgh efg aceh befgh gh afgh abeg abcfh acf ach abeg ch abfg ceh cefg abfh cfh acegh ace bgh fh aefg bch bef abch befg beg bfgh abegh ce abcgh abceh abceg fh cg bcef abceg i abe ae abcefgh bcfg ce beg acfh efg e bcegh abceh ae abegh acefh abgh ae abeg cef abfg bef abeg abch e abeh ae egh e beg ae abeg abef acefg ach efg abcef ce abfg bcfgh bfg abcef abcgh bef eg fh cfgh abceh eg bfg fgh abcgh abceh efg abcef aeg bcef ace aeh abcfg bfh afgh abegh beg acefg abceh egh abef aeg ae acfgh beh beg bef afgh h abcef cgh abcefh bgh beh fgh abeh acg i beg bcef abcefgh abcef beh begh abeh acg aceh beg ceh acg fh bcefgh i bfh acg beh abfg abceh acgh bceh cfgh f bef ch aefg abfgh ceh bcfg bceh aeg abceh eg abcef beg cfgh cefg egh bceh bcef ae efg bceh aeg aefgh abeg i cfgh bcef eh egh i g abcefh cegh h acegh i acfgh abi bcefgh aegh bfh acfgh aefh cg bci bfgh i bcefgh bef ace abegh cfgh abcg bi abc abef beg afh afgh ci aceg abfgh eh bcgh abef g i ag aceh aceg ceh i cef aceh g bci bcg acf g ci cegh bceh beg aef acfgh egh bceh ace ceh acg bei cg bci efg beh bceh befgh bci acg abcef gh afh acg i cg cefh bef acefh abci beg bci bg befh aegh bci ag acefh aefg abeh ag abefgh e cg bef ag bceh g ceh ag i befgh fgh acfh bcefh i aegh cefh ag acefh abfgh abcefh cegh abfi i cfgh ai ag abef cg ai cegh bceh acefgh aci bcgh acfgh abi fgh ai acg abi g aci ag befh aegh abefh bfg bcfgh ci abcgh ai bg i cg ai acg abcei abfg bcefgh bfg egh i g ai abefgh i g ai ag afgh abcef cfgh bfh ag bcefh abfg acfh bcfg i befgh afi abei ag i acegh ai ag acefh g ai acg ci bcegh cfgh abcei egh abcgh g ai abegh abcef abcfg aci bfg abci abfg gh aci afgh i abcgh ai egh i abgh ai bfg beh aegh abgh ai ag i aegh efh bcgh i abfg acfi ai ci acefh abgh ai bcgh ci abcfg bi ai ci bcei cfgh bcfg abegh cfi abfg bi bgh fi cgh abcei bcg afgh befi acegh abcei abegh abcfi abcfh abei bgh abfi bcei ah abcei afgh abcfi abgh abcei bgh ci bcegh afi abefgh abh aegh afi ai abcegh bei aegh acg bcgh cfi acei acfi bcef afgh cg abcgh acg bgh abi abcgh aci acfgh aei cfgh aci ei bceh ci abgh bi bgh fi acegh abcei cegh bcei abcfg abfgh ei bgh aei abgh abei bgh befi beg bfi bfgh cefg g abgh ai bgh i abgh cei cegh cfi acei beg cegh abch acei abcgh cei agh ci gh aci agh ci bcei ae bci bcgh aei gh bi agh fi fgh cefh egh fi ci abcgh bi afgh abi gh bcfi cegh abfi abgh afi abcei bgh acei cgh abei bgh bei acegh abei bi bcefi aei bfi ceg bgi bei cgh ei agh befi abcgh bi abcefgh befi aei abcei abefgh bgh ci gh bcfi agh bcgi gi abcei bgi acefi acei gh abcei bcgh bcei gh bcfi bcgh abfi fgh bcfi abcei bgh bcei gh cei bgh bcei abgh ah abcei abcfi ch acegh abcei bgh bcei abgh abei bgh aei abfgh ei acfgh bcgi cfgh cgh ei bgh abfi bcfh efi bgh abi bei abefi abei egh egi abcgh cei agh abi gh bcfi abceg acefi abcgi cefi abeg acefi bcei acegh cei bgh aefi abgh abcei bgh aefi abfgh abcgh abcei h fgi abgh cei bcgh aefi abgh bfi bgi ch abgi abgh bci bgh acei cg efi bgh aefi acegh cefi agi egh acei abcgh cei bfgh bcei abgh afi bgi aefi abfg acegh c bgh acefi abgh ai bfg acei bfh bfi afgh aefi bfh aegh bcfi bgh abfi fgh cei bgh aefi abgi abcefi aegi egh abfi abcg cei bgh abcfi abfgh abei bfgh bcefi fgh abcei bfi bgh i acegh abcei bcgh bceg fgh afi afgh egh acefgh abcgh bfi cegh acefi aegh bcfi afgh aefi befgh abcfg afgh abefgh ci acegh abei bgh ag fgh bcfi afgh cfi abfg ai bgi egh bcei abgh bfi afgh abfi fgh bfi bfgh egi aegi acegh bfi cegh abci aegh bi abcfh bei bcefgh efi afgh abegi abgi abcgh bfi egh i abcgh afi afgh bei befgh aefgi afgh egh fi aegh afi egh abfi aefgh aci abefgh i abcfi begh bcfi bfg i abfg bi cegh i befgh cei ag acei abfi aegh bfi bgh i aegh ai acfgh i cg aegi abcefgh abefgh cfi abcgh ai bcgh i acegh befgi abcefgh abcfi bcegi bcefgh ai acg abfi aegh aci abegh ci abgh bfi bcfgh cfi cfgh aegh aci acg fi aegh aci abefgh aefi befgh abgi bcfgi abefgh cfi aegh acfi bgh i fgh bci abcfh ach begi bfi abegi egh cfi acegh afi abegh fi aegh cefg cefgh acgi abfi acegh acfi egh abfi abgh aci afgh efgi aefgh bfi bcfgi i abeh begh bfi afgh abi aegh ei abcegh i abgi acfi abcefgi efgh cfi aegh bfi egh cfi abgh aci abcefgh i abcgi aefgh bcfi egh bcei aegh ch egh abfi fgh abcei aeh acfgh cfgi abcgi achi bcgh abfi begh bfi egh ci acegi abgi cefg agi befgi fgh ei abegh ci aegh aci acfgh ci befgh begi acefh afgh abcfi bceg bci bcfgh ci abfg abgi beh abfi hi abgi efgi ae bcei abgh achi bcgi abhi bcefgh bi beh bgi abceh fgh abcei agi bei gh achi acfgi bcei acegh gi efi bfgh bei abcgh abei cegh efh befgh bcfi abefgi cefh bch ahi cefi abegh abeh abgh aefh egh acei cgi bcegi egh agi befi abfgh abefgi afgh bei aegh ei abefgi bei cfgh fgh ch abcegh eh abcgh ch bcgh hi bcefgh cei abefg bfgi eh aegi aeh acfgh bcei aegh cei bcgh cefh g abei acfgi aei bcei gh bfi efg acei acefg aci acgh acefi hi aegi aeh bgi aehi cgh abcei acgh i abgh abcefi bgh chi cfgi abei acef bcgh bei cgh aeh bgh bcei acegh bhi abcefgi abhi cfgi gi aeh cefg eh cgh aefh bcgh acei cfgh efi bcef abcefh aefi begh beh acgh ceh abcgh abei bcfgh efh abeh abcei bg cegi ceh aegh ag egh efh beg aefh afgh hi acefgi gi beh egh ah abgh bcefh bfgh bcfh abceh acefh abei bcehi ceh abgi bceh ce bcei cfgh ai bcgh abefh abcfgh acefh abch bfgi ceh abcgh acefh agh abi abcgh acefh bcgh bcfg ah afi achi bcgh ci abcgh aceh bgh abeh abgh cei bfgh cegi bfh gi acefh afgh ah acegh aefh bcfi aehi ach bcegi h cefh bcfh abcgh abcei bcgh bcfh gh aefh bcgh abefh beg ehi abfh abefgh bfh cfgh bhi bfgh cefh fgh aci abeg bgi afh cg abch bcgh ach abcgh fh bgh cefh aegh abfg abfh acefi ach gh abfh cegh acefg abgh aefh egh hi fgh acefgi h abefgh cfi abgh acefh bgh afh abfg acefh ag egi bfh efi abcfh bgh acfh acegh afi bc cefh fgi acefh acfgh abfhi g aegh ch acfgh cefh abgh h afgh abhi bcefgh ahi abfh bfgi afh abgi h cegh bcfh fgh aefh abefgh hi fgh cfgi abcfh afgh bch bcegh abch abcegh ach abcfgi ahi abeg afgi abeh abgi ch abcegh bh abfg cfh bc afh abcg bcfi bcfg egi bcfh abgi h acg bfh g bcfi bcfgi abcefgi fgi acegh abcfh abegi bh cfgh abfh bgh ah acegi cfh bcfhi afgi acfh abgi abfh egi afh abgh cfh ag hi fgi bcfi cfh bcgi bfh abgi h bgh bfh abgi abfh bg bfgi g befgi cfh efg acfh aegi fh ag e beg ahi egi af cefh abcgi fh egi bh fgi fh acg hi cg achi acg ah bfh cg abcfh ag afh g abfh abefgh hi af cehi abcfh bfg af fgi h ag afh acegi aci acefh hi cefh abfgi abfh afgh aefg befgh ch abceg abhi bcef h ag bcfgi bcfh abcgi ch acg bfh fgh h acfgh bh abg abfh bceh bcgi abceh abgi h bfg bfh bceg aci acg abchi efh abcfgi acefh abef bfh bceg abch cegi ach abghi ahi acg egi g abcfgi aefh egi abeh abcfgi h bgi ce aefgi bi acefh bef abefh fgi abh bgi bc cfgh h abcehi ach abcefh ch bceh abci abeh abgi beh acfgi ah acefgi aceh acefh abeg cg befgi beh bgi abceh aci h bgi ah aegi af bfg egi acfh aceg abch abceg ah abgi ch cegi abceg efh ch aefh bcgi ceh beg h abcfi abceh bceg bcfi afgi chi abefh afhi aefh abef ach abgi ch bgi eh aehi h abei acehi efh bi aefh egi eh acefg beh bcgi ceh acefg acegi acefh abi abeh ai beh e abeh abcgi abh abefgh abcegi abfg bcegi bceh acfgi abceh ai aeh abci abceh abcgi ahi bcfgi bcgi aefg beg aceh abcef ceh bcef ch egi ach fgi afhi ag bcgi abeh e aeh bgi abeh abgi ahi bcfg hi abcfg abc f abeg eh ce h cefg ceh abgi bfhi aghi bcehi aefgi beg beh acg eh cgi bce abceg abeh bcei bceh bfg ci abeh abgi aeh cefg eh aefg beh aghi af acegh abcgi aceh abeg eh f h abceg eh bef bhi bfg bgi hi cefi abh cefg abeh beg beh efg abeh aefg aceh efg ceh acf beg h bcfg ah aegi beh bgi eh aefg bceh cefg cegi ach efi beh aefi abeh beg fh bcfgi abceh acefg cg efg abeg ah beg aceh bcgi abceh abcgi achi cefg chi cfgi gi h aefi ah g ae bcgi bch acefg abcgi h acg ah cgi abfh efg abcef bceg ab efg e bceg aefgi h ci ah cg h efg abeh aefg ahi cefg aefhi acefg bceh abh abegi ach abcgi bceh afgi bc abfg afhi cefg i af abgi h bgi bh abgi aceh bfgi bc bh abc ace agi e acefg bcef efg bch abcgi ch abeg abef aefg efhi h abefgi ah abgi h abceg ach beg abcfh cehi egi ach acegi h bcgi ah befgi ch efg ef abcgi abcfh ch afgi ah acefg bceh bgi ach abcgi h abeg behi bceg bcef abc acg ah abgi cf bcfg bch beg abcfh abefgi efgi acefg abgi abh bcfg acf abcfg abc cef abef abcei abcfg f abegi ah abcfg h ag e abcgi ae bcgi bcfh cg abfg h egi ah g abh ag ah befgi bcef abefgi b aefg acefh aeh acg bh cg h acg bh bcefgi f abcehi ce ah cg h acg ah abceh h bcgi afh befgi bfhi beh bcfg ah g h bfg ah beg f bgi abe eh abfh beh agi abef abfg ch cegi e cg cf abeg cefh abeh cfgi ch bcfg ach abcfg acef bcei bfh abceh abcfg bceh bfg bceg aegi aef cegi ach abfg bef acg ce bceg abfh ae egi ceh aegi abfh cegi ah b acef abc bfh ah acegi aeh aegh afh g fh beh bc cg bcef ag abefgi ah g ch abeg afh g cf bfg bfh abcfg abcfh acefh bcg eh abcgi ace bgi ef beg bcef abeg abcef cefh bcef bceh ag abceh g abcfh ag abcef g acef beh abcgh bc abgi abfh abeg ceh fgi ae bcgi e befgi fh aefh ag abeh cfg ae bgi abef aefg fh bfg acf g abcfh beh acfgi ach fgi abc ag bcfh cg abcfh acg bcfh efh abcfh abch abefgi eh cg aefh cegi abcef efh abcfh beh cefg af beg h ag acf g ae abeg abceh g acefgi abeg abefgi ceh g ab abeg ef gi bef acefh acfgi abfg abcfg f bcgi ach abgi abcfh ahi bfh aegi abcgi acefh bcehi abceh abgi cf bgi eh cgi bef bcei cefh bcehi ehi beh abef acf bceg bcef abeg abef gi cf egi aegh abeh abcgi cf bcgi ce cg aefh afgi ah bfi bcef bfhi acf bfh abgi beh abeg efh g bef aghi cefh gi bcef acefi abefgi abeh abcgi bcef acg abceh gi bcef ceghi abcef af beg bcef abceg af cg beh agi abef bceg aefh bgi cefh abfg befgi bfg abceg ceh cg aceh acg cefh gi bef abfh abceg abef bceg beh agi ceh gi cf acei abcef abef ace bceh agi abceh gi bcef agi cefh fgi abf cefg cefi abeh abfgi ace abceg abef abgi ace bgi acf abgi ehi bcgi cegi bfh gi bceh abceg abef afgh cfh acfgi ah befgi beh abceghi agi abeh gi bcef acg acf abcgi aefh abfh aefhi abef abehi bef abeg abeh beg bceh abeg hi bfh beg bcef bcgi bcfh cg bcef bgi bf abcgi acef abcegi abcef bcfh abcefhi ch abeh acf abcgi bcef abceg ce bceg bhi bcef ef abfg egh h acefgh afh afgh abc acg bcfh cfgi bhi cfh acg abef bceh h bcgi acf abcgi fh bcfgi ach abcgi abcfi cfh cefgi ef bceh bcef afgi afh ghi acefh bfg abefgi bcfi bcefgi aef bcgi ah abcgi abch bcefgh bcfh abgi bhi acefi abeh ah bhi ch befgh bfh aegi bcef cegi hi acegi abefhi abcfh abeh ach abgi h ag ah abgi ch cegi acehi abcefgh beh h cefi ach cgi abc egi bc abcghi abc aghi chi acfh bcefgi aef cefgi abcef afgh bcef bcgi abeh ghi abfh abcfi acehi bh aegi ch cegi ach ghi abh abefgi abeh abgi achi ch efgi ach abcgi abch aghi ah beghi h aefi acfh ach afhi h aegh ach aegi h acgi abei ghi abfh bgi abchi bch abfg aefi efgi ach aegi h befi cefi bceghi befgi ch bcefgh ach befgi h acgi ach aefgi abfh aghi ah bceghi cfghi acefi abcfhi abcefi ghi h egi bcfh abfgi abfh egi bcefgh bfi fgi beh aghi ah aegi h abefgi ach bcfi abehi aefh chi abeh aegi fh bgi chi abgi h aghi ach bcfi aefh aceh abcfhi cefi abgi abcfh bcgi ach beg ch aghi ach abcgi cehi acefi acehi ach abcgi h beh ach ghi

Monoid Structure