Details Page for 0.7306

Complete Solution is Known:

MSV File: q-0.7306.msv

Growth Pattern:

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Details for Q₁₀₀₁(0.7306):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p | a²=1, b³=b, bc²=b, c³=c, bd=ab, c²d=d, d³=ad², be=bc, c²e=e, d²e=cd², de²=ad², e³=ce², bf=ab, c²f=f, d²f=adf, ef=acdf, f²=b², bg=bc, cg=e², dg=acd², eg=e², fg=acdf, g²=e², bh=bc, d²h=adh, eh=ch, dfh=afh, gh=ch, h²=b², bi=ab, c²i=i, d²i=adi, ei=ci, dfi=afi, gi=ci, di²=ab², fi²=ab², i³=ai², bj=ab, c²j=j, dj=b², ej=cj, fj=b², gj=cj, ij=aj, j²=chi², bk=bc, c²k=k, dk=acfi, ek=ck, fk=ab²c, gk=ck, i²k=aik, k²=b², bl=ab, c²l=l, dl=b², el=cl, fl=b², gl=cl, hl=hj, il=al, l²=b², b²m=m, c²m=m, dm=am, em=cm, fm=am, gm=cm, hm=cm, im=am, jm=am, km=cm, lm=am, m²=b², b²n=n, c²n=n, dn=an, en=cn, fn=an, gn=cn, hn=cn, in=an, jn=an, kn=cn, ln=an, n²=b², b²o=o, c²o=o, do=ao, eo=co, fo=ao, go=co, ho=co, io=ao, jo=ao, ko=co, lo=ao, o²=b², b²p=p, c²p=p, dp=ap, ep=cp, fp=ap, gp=cp, hp=cp, ip=ap, jp=ap, kp=cp, lp=ap, p²=b²>

P = {a, b², ac, ac², d², ae, ace, e², df, g, h, ch, acdh, acfh, ci, acdi, hi, adhi, i², chi², aj, achj, ack, ahk, cik, hik, cjk, al, jl}

Phi = 1 a b ab b² c ab d e b f g b bc h b bc i b ab j k ab l b²c ab l b²c ab b b²c ab²c b abc ab²c ab abc ab²c ab bc ab²c ab bc m ab bc m b²c bc abc b²c bm abc ab²c bm bc ab²c b²c bc m b²c bc m ab bc abc ab ab² abc b ab² bc b b²c bc b b²c m b ab m am ab ab² am b ab² bcm b abm bcm b abm bcm b ab bcm ab² ab bc ab² ab bc ab² ab bc ab² bcm bc am bcm ab am ab² ab bc ab² ab bc ab² ab bc ab² b²c bc abc b²c ab²c abc ab² ab²c abc ab² b²c abc ab² b²c bm ab² ab²c bm bc ab²c bm bc abcm bm abc abcm b²c abc m b²c acm m b²c acm m b²c ab²c m n ab²c ab² n ab²c ab² bcm ab²c abm bcm n abm abcm n abm abcm ab abm ab² ab n ab² bc n acm bc ab acm ab² ab bm ab² n bm ab² n ab ab² abcm ab cn abcm ab cn ab² ab bm ab² b²c bm ab² b²c b ab² b²c b n b²c b n am b ab am bn ab abc bn bm abc m bm n m ab² n am ab² n am bcn n an bcn bm an m bm abm m acm abm abc acm amn abc m amn abcm m b²c abcm ab b²c bn ab ab²c bn abcm ab²c bm abcm ab²c bm abcm ab²c b²c abcm n b²c bm n ab bm abcm ab mn abcm n mn bcm n b²c bcm cmn b²c bn cmn abc bn bcm abc acn bcm n acn bcm n cm bcm ab² cm acm ab² abm acm ab² abm acn ab² bm acn ab² bm abm ab² bcn abm n bcn ab n m ab acn m bm acn m bm amn m cmn amn n cmn ab²c n m ab²c amn m o amn m o bm m n bm abcm n cm abcm m cm bm m acm bm m acm bn m n bn cmn n acm cmn abc acm acmn abc cm acmn bc cm acm bc n acm bc n acm bc bcm acm o bcm cm o bcm cm acm bcm abcm acm ab² abcm ab ab² abcm ab m abcm bn m ab² bn n ab² bn n m bn b²c m abcm b²c m abcm b²c m am b²c o am bn o am bn bm am ab² bm cmn ab² bm cmn am bm cmn am acm cmn am acm abm am m abm cmn m ab cmn m ab ab²c m ab ab²c ab² ab bn ab² m bn abcn m acm abcn m acm bcn m acm bcn m acm cm m bc cm abcn bc o abcn ab² o b²c ab² acm b²c abcm acm abcmn abcm o abcmn abn o abcmn abn abcm abcmn bo abcm mn bo cmn mn ab cmn mn ab am mn abm am abcn abm n abcn abm n m abm n m abn n m abn bm m bo bm n bo o n m o ab²c m bco ab²c an bco amn an bco amn abcm bco acm abcm abo acm mo abo bcmn mo an bcmn bm an bc bm o bc abco o ab² abco b²c ab² abco b²c ab² abco bco ab² bc bco m bc bm m ab² bm mo ab² abco mo bcm abco ab bcm co ab abmn co ao abmn aco ao abo aco abm abo am abm ab am o ab amo o bm amo ab² bm acn ab² ao acn n ao ab n o ab m o b²c m ab² b²c abcm ab² bm abcm n bm ab n cmo ab aco cmo bm aco bc bm b²c bc bcmn b²c bc bcmn b²c bc bo b²c aco bo abmn aco ab² abmn aco ab² bcmn aco co bcmn mo co bcmn mo aco bcmn ab aco cmo ab aco cmo bmn aco ab² bmn abcmo ab² o abcmo ano o b ano aco b abo aco bcmo abo ab² bcmo ab ab² ano ab abo ano b²c abo ab² b²c n ab² co n ab² co n ab² co n bc co ab bc bcmn ab bcmo bcmn ab²c bcmo abc ab²c bcmo abc amo bcmo m amo b²c m bcmn b²c abo bcmn cmn abo abc cmn o abc abcmn o abmo abcmn b²c abmo bcmn b²c abcm bcmn mo abcm bc mo co bc an co abc an amo abc bn amo bmno bn cm bmno bmo cm abco bmo ao abco abcm ao b abcm bn b ano bn ab ano bn ab no bn bcno no amn bcno abmn amn bn abmn bcmn bn ab bcmn bn ab cno bn ab cno bn ab aco bn abcno aco ano abcno ab ano abcm ab bmno abcm b²c bmno m b²c bn m n bn bcmn n b²c bcmn m b²c acmn m ab acmn ab² ab cmn ab² bmno cmn abcm bmno b²c abcm bcmn b²c bm bcmn b²c bm abno b²c bmno abno ano bmno bmo ano b²c bmo acmno b²c bcno acmno b²c bcno abcm b²c bmno abcm amo bmno ab² amo cm ab² bcm cm cmo bcm ab cmo bmo ab abmno bmo cmn abmno ab² cmn ab ab² b²c ab m b²c ab m co ab bmo co ab²c bmo ab² ab²c ab ab² abmno ab bc abmno abm bc am abm acmno am bn acmno abc bn bm abc abcmno bm abmo abcmno abcmo abmo m abcmo bm m mo bm abc mo bm abc m bm abmo m acm abmo m acm bn m ab bn abcm ab bm abcm m bm bcno m ab bcno abcm ab bn abcm p bn abcm p bn abcm abcmo bn bo abcmo acm bo bcm acm cmo bcm ab cmo ab² ab cm ab² bo cm cmo bo p cmo abcm p cp abcm b²c cp ab² b²c cno ab² abcn cno p abcn bm p abcm bm p abcm bm p acn bm mno acn bcno mno m bcno bn m n bn abmo n ab²c abmo m ab²c bm m ano bm abcm ano ab²c abcm m ab²c bo m amo bo m amo bno m bcmo bno abcm bcmo p abcm abp p mno abp abmn mno abcm abmn abco abcm ano abco aco ano ab aco n ab abcmno n cm abcmno m cm bcmn m bcmo bcmn abcno bcmo acm abcno abcm acm p abcm abco p n abco p n bm p bc bm acm bc abcm acm bcmn abcm p bcmn bo p abmo bo p abmo am p abm am bmp abm amp bmp b²c amp m b²c amno m bm amno am bm abm am bmno abm cmo bmno bm cmo m bm bcp m acm bcp abcm acm bm abcm mo bm ab² mo acm ab² n acm p n cm p abcm cm p abcm bcmn p abcm bcmn ab abcm acmno ab p acmno bcp p bcm bcp acm bcm abcp acm bo abcp cm bo acmno cm n acmno bm n abcm bm amp abcm amn amp m amn acn m bmp acn co bmp ab²c co n ab²c p n acp p bc acp b²c bc cp b²c mp cp bm mp n bm mp n bmp mp cmn bmp bm cmn bcmn bm cmn bcmn acn cmn am acn cmn am acn cmn bo acn p bo bmno p cmn bmno ab cmn bcno ab cmn bcno o cmn abcm o ab abcm o ab abcm o ab abcm bcm ab cmn bcm abco cmn abcn abco bcp abcn cno bcp m cno acm m cno acm m cno abno m abcm abno bcp abcm ab² bcp np ab² bm np abcm bm acn abcm bm acn bp bm bcmo bp bn bcmo bmn bn abm bmn bc abm bp bc o bp bc o mp bc abmp mp abo abmp abm abo bmno abm b²c bmno amo b²c ab² amo bm ab² abcmno bm ab² abcmno acn ab² bcmn acn abmo bcmn cm abmo abcm cm p abcm abcmno p ab² abcmno bmno ab² bcmn bmno ano bcmn ao ano ab² ao p ab² bcmn p cmn bcmn acm cmn ab² acm bcmp ab² amp bcmp abcm amp abcmno abcm bp abcmno abo bp amp abo amn amp bo amn o bo ano o bcp ano o bcp abc o aco abc bp aco bcp bp bm bcp abc bm bcno abc amo bcno abp amo ab²c abp bco ab²c acmno bco n acmno bcmn n acmno bcmn bcmo acmno abp bcmo abcn abp bcmo abcn acn bcmo ab acn bc ab aco bc bco aco bc bco ap bc bp ap abmo bp ab abmo bn ab cno bn ab cno abmo ab cmn abmo bp cmn abmo bp ab abmo cno ab cmo cno bcmo cmo bc bcmo abmn bc mno abmn bc mno b²c bc cmn b²c bcmp cmn bcmo bcmp bc bcmo amp bc np amp bo np amp bo cno amp abnp cno p abnp acn p abcp acn bmp abcp m bmp p m bmp p aco bmp amo aco bc amo cnp bc ab cnp ab² ab b²c ab² n b²c abnp n acm abnp bc acm aco bc ab aco ab² ab n ab² abp n ab² abp amo ab² bc amo np bc amo np ab² amo b ab² bp b cno bp acmno cno bmp acmno bc bmp amo bc cmo amo ab cmo abp ab cmo abp abcn cmo abp abcn amp abp bn amp bc bn bcp bc acp bcp bc acp abcn bc cp abcn mp cp ab²c mp bc ab²c mp bc cp mp abmo cp b²c abmo bc b²c acnp bc acm acnp mno acm abcn mno ab abcn abmo ab b²c abmo bp b²c cmn bp bcmn cmn bno bcmn cmn bno acmp cmn abmo acmp no abmo bc no amp bc ano amp bn ano ap bn abp ap amnp abp bmno amnp bp bmno bo bp ab bo bn ab acm bn bm acm acp bm acmno acp bp acmno bcmn bp abcp bcmn ab² abcp amp ab² b²c amp ab² b²c bcp ab² bp bcp abc bp bcmo abc m bcmo abcp m abnp abcp acn abnp b²c acn m b²c abmnp m b²c abmnp abcmno b²c bn abcmno bcnp bn bc bcnp bcp bc n bcp ab² n abco ab² bp abco cmn bp n cmn abmp n mno abmp acnp mno bn acnp acmnp bn abcn acmnp bo abcn o bo abcn o p abcn o p bcmp o bm bcmp abcn bm bcmp abcn bm bcmp aco bm acn aco bcmo acn bo bcmo bm bo cp bm acn cp bcmo acn m bcmo abno m bcmo abno bcmn bcmo bm bcmn m bm cn m b²c cn cmo b²c anp cmo abmp anp bop abmp cmn bop abmn cmn mp abmn p mp acp p bm acp abcnp bm aco abcnp bn aco bmno bn ab² bmno abco ab² bc abco mp bc n mp amop n abco amop bp abco mno bp abop mno bcm abop abcp bcm acnp abcp abcm acnp bm abcm bp bm m bp bm m abmp bm amp abmp bm amp bo bm acn bo abcn acn bo abcn abm bo ano abm bcmn ano op bcmn bo op amp bo acmp amp acn acmp o acn abcn o cnp abcn mop cnp am mop abm am abmp abm aco abmp bm aco bcmn bm cop bcmn abco cop abcm abco mno abcm m mno abcm m abco abcm bc abco cmn bc abco cmn aco abco abcmno aco acp abcmno abcm acp abcmno abcm n abcmno cop n abco cop bcm abco abcmno bcm acnp abcmno bcm acnp bcmp bcm bcno bcmp m bcno bcmn m abcn bcmn abco abcn o abco m o acm m bcmo acm bo bcmo bcmnp bo abmp bcmnp p abmp abno p abc abno bn abc bcnp bn abmn bcnp bm abmn bo bm abcp bo bmp abcp m bmp bm m bmp bm np bmp bm np m bm abcp m abco abcp bc abco bn bc bcmn bn bcno bcmn amo bcno bp amo p bp acm p abcm acm abcmp abcm bcmn abcmp bcm bcmn abco bcm cmp abco p cmp bcmn p abcm bcmn bcnp abcm o bcnp abcm o cm abcm abcn cm m abcn o m acmno o acm acmno bm acm bc bm abco bc op abco abmn op bm abmn bo bm abcp bo bm abcp m bm o m abcn o acop abcn o acop bcmn o bcno bcmn abco bcno m abco bm m bcmn bm abcm bcmn amnp abcm m amnp cmn m abco cmn m abco p m bp p ab² bp abco ab² ano abco cmn ano bp cmn bcno bp amo bcno bp amo abcm bp ab abcm aco ab anp aco bcmn anp cmn bcmn amo cmn o amo p o cno p aco cno m aco bm m abnp bm abmn abnp o abmn m o amp m acp amp bcmp acp b²c bcmp cmo b²c np cmo amn np bo amn cmn bo abcmno cmn abcp abcmno amn abcp abmn amn b²c abmn acp b²c abmo acp b²c abmo cno b²c bcno cno acmnp bcno abo acmnp amp abo acm amp abcm acm abco abcm bcmn abco aco bcmn cm aco bcmnp cm p bcmnp bcmn p ab² bcmn amo ab² acmp amo abcp acmp bp abcp ab² bp amo ab² bp amo amnp bp acm amnp cp acm bcp cp bcmo bcp abcn bcmo ab abcn abp ab abmp abp ano abmp abp ano m abp abmop m cmo abmop m cmo bp m abo bp b²c abo bp b²c abmn bp b²c abmn bcmn b²c bcno bcmn abco bcno bcmn abco abcn bcmn acp abcn p acp ab p cmo ab bn cmo bmno bn bcmn bmno o bcmn cp o aco cp abcmno aco cmp abcmno bn cmp n bn abmo n bcmp abmo cno bcmp aco cno n aco ab² n p ab² bcmn p bc bcmn acn bc bp acn bn bp ab bn bp ab bcmp bp bcmo bcmp aco bcmo abmn aco cmp abmn aco cmp b²c aco abcm b²c abcmno abcm abcn abcmno abcm abcn ap abcm abcn ap m abcn cmn m cmo cmn acn cmo cmn acn abmo cmn mp abmo aop mp ab² aop cmn ab² acmnp cmn bcp acmnp abmp bcp ab² abmp p ab² m p co m o co bp o bn bp b²c bn mno b²c bcmo mno n bcmo mno n p mno acmnp p cmn acmnp n cmn abcn n acn abcn bcmo acn bn bcmo ano bn abcn ano bn abcn ano bn abcn ano acn abcn cmp acn aco cmp abmn aco bmnp abmn bo bmnp bcmo bo cp bcmo ano cp abcn ano aco abcn abcmnp aco abno abcmnp abmnop abno cmn abmnop bmno cmn abmn bmno b²c abmn bc b²c bcno bc bmno bcno abmo bmno b²c abmo bmno b²c bm bmno b²c bm bo b²c cmn bo bmno cmn bmo bmno acmnp bmo bmno acmnp bn bmno acm bn aco acm p aco n p aco n acn aco bp acn abmop bp abco abmop aco abco abcmp aco bcmo abcmp bo bcmo acn bo aco acn bcmp aco o bcmp aco o bmnop aco b²c bmnop aco b²c abcmnp aco acmno abcmnp bc acmno cmp bc acmnp cmp amp acmnp bcno amp m bcno mp m cp mp acn cp abno acn cno abno bn cno abmp bn abcm abmp mno abcm n mno abmo n abco abmo n abco abmo n amo abmo bo amo bn bo m bn abmo m cop abmo m cop bn m cop bn aco cop p aco abcop p bn abcop amo bn bcno amo ap bcno bop ap bo bop abcmno bo cmp abcmno bo cmp abco bo abcm abco abcmno abcm o abcmno abcn o abcmno abcn o abcmno cmo o abcmno cmo abcm abcmno abcmp abcm bcmo abcmp bo bcmo mp bo abcn mp bo abcn

Monoid Structure