Details Page for 0.7122

Complete Solution is Known:

MSV File: q-0.7122.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₇₈(0.7122):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s | a²=1, b¹⁹=b¹⁷, bc=ab³, c²=b⁴, b²d=b⁵, cd=ab⁵, d²=b⁶, b³e=b⁷, ce=ab²e, de=b⁷, e²=b⁸, b⁴f=b⁹, cf=ab²f, df=b³f, ef=b⁹, f²=b¹⁰, b⁵g=b¹¹, cg=ab²g, dg=b³g, eg=b⁴g, fg=b¹¹, g²=b¹², b⁶h=b¹³, ch=ab²h, dh=b³h, eh=b⁴h, fh=b⁵h, gh=b¹³, h²=b¹⁴, b⁷i=b¹⁵, ci=ab²i, di=b³i, ei=b⁴i, fi=b⁵i, gi=b⁶i, hi=b¹⁵, i²=b¹⁶, b⁸j=b¹⁷, cj=ab²j, dj=b³j, ej=b⁴j, fj=b⁵j, gj=b⁶j, hj=b⁷j, ij=b¹⁷, j²=b¹⁸, b⁹k=b¹⁷, ck=ab²k, dk=b³k, ek=b⁴k, fk=b⁵k, gk=b⁶k, hk=b⁷k, ik=b⁸k, jk=b¹⁷, k²=b¹⁸, b⁸l=b⁷k, cl=ab²l, dl=b³l, el=b⁴l, fl=b⁵l, gl=b⁶l, hl=b⁷l, il=b⁷k, jl=b⁸k, kl=b¹⁷, l²=b¹⁸, b⁷m=b⁶l, cm=ab²m, dm=b³m, em=b⁴m, fm=b⁵m, gm=b⁶m, hm=b⁶l, im=b⁷l, jm=b⁷k, km=b⁸k, lm=b¹⁷, m²=b¹⁸, b⁶n=b⁵m, cn=ab²n, dn=b³n, en=b⁴n, fn=b⁵n, gn=b⁵m, hn=b⁶m, in=b⁶l, jn=b⁷l, kn=b⁷k, ln=b⁸k, mn=b¹⁷, n²=b¹⁸, b⁵o=b⁴n, co=ab²o, do=b³o, eo=b⁴o, fo=b⁴n, go=b⁵n, ho=b⁵m, io=b⁶m, jo=b⁶l, ko=b⁷l, lo=b⁷k, mo=b⁸k, no=b¹⁷, o²=b¹⁸, b⁴p=b³o, cp=ab²p, dp=b³p, ep=b³o, fp=b⁴o, gp=b⁴n, hp=b⁵n, ip=b⁵m, jp=b⁶m, kp=b⁶l, lp=b⁷l, mp=b⁷k, np=b⁸k, op=b¹⁷, p²=b¹⁸, b³q=b²p, cq=ab²q, dq=b²p, eq=b³p, fq=b³o, gq=b⁴o, hq=b⁴n, iq=b⁵n, jq=b⁵m, kq=b⁶m, lq=b⁶l, mq=b⁷l, nq=b⁷k, oq=b⁸k, pq=b¹⁷, q²=b¹⁸, b²r=bq, cr=abq, dr=b²q, er=b²p, fr=b³p, gr=b³o, hr=b⁴o, ir=b⁴n, jr=b⁵n, kr=b⁵m, lr=b⁶m, mr=b⁶l, nr=b⁷l, or=b⁷k, pr=b⁸k, qr=b¹⁷, r²=b¹⁸, bs=r, cs=abr, ds=bq, es=b²q, fs=b²p, gs=b³p, hs=b³o, is=b⁴o, js=b⁴n, ks=b⁵n, ls=b⁵m, ms=b⁶m, ns=b⁶l, os=b⁷l, ps=b⁷k, qs=b⁸k, rs=b¹⁷, s²=b¹⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, d, be, f, b²f, bg, b³g, h, b²h, b⁴h, bi, b³i, b⁵i, j, b²j, b⁴j, b⁶j, bk, b³k, b⁵k, b⁷k, l, b²l, b⁴l, b⁶l, bm, b³m, b⁵m, n, b²n, b⁴n, bo, b³o, p, b²p, bq, r}

Phi = 1 a b a 1 ab 1 ab b a b c 1 ab ac ab³ b c d abd b² ad e abe b³ ae f abf b⁴ af g abg b⁵ ag h abh b⁶ ah i abi b⁷ ai j abj b⁸ aj k abk b⁹ ak l abl b¹⁰ al m abm b¹¹ am n abn b¹² an o abo b¹³ ao p abp b¹⁴ ap q abq b¹⁵ aq r abr b¹⁶ ar s ar b¹⁷ as

Monoid Structure