Details Page for 0.7135

Complete Solution is Known:

MSV File: q-0.7135.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₃₁(0.7135):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x | a²=1, b³=b, b²c=c, c⁷=ac⁶, bd=ab, cd=ac, d²=b², b²e=e, c²e=abc³, de=ae, ce²=c³, e⁵=bc⁶, b²f=f, cf=abce, df=af, ef²=abe²f, f⁵=ac⁶, b²g=g, c²g=ac⁴, dg=ag, ceg=bc⁴, e³g=abc⁶, e²fg=ae⁴f, f³g=ae⁴f, cg²=c⁵, e²g²=c⁶, fg²=e⁴f, g³=ac⁶, b²h=h, ch=abcg, dh=ah, e²h=ae³f, f²h=bf⁴, fgh=abe⁴f, g²h=bc⁶, h²=f⁴, b²i=i, ci=cg, di=ai, e³i=abc⁶, efi=efg, f²i=abefg, egi=eg², fgi=egh, g²i=abeg², ehi=e⁴f, fhi=abegh, ghi=eg², ei²=bc⁶, fi²=egh, gi²=abeg², hi²=bc⁶, i³=ac⁶, b²j=j, c²j=abc⁵, dj=aj, cej=c⁵, e²j=bc⁶, efj=egh, f²j=abe⁴f, cgj=bc⁶, egj=abeg², fgj=bc⁶, g²j=bc⁶, hj=ae⁴f, eij=ac⁶, fij=eg², gij=eg², i²j=bc⁶, j²=c⁶, b²k=k, ck=abcj, dk=ak, e²k=e⁴f, efk=abegh, f²k=ac⁶, egk=eg², fgk=ac⁶, g²k=ac⁶, hk=abc⁶, eik=bc⁶, fik=abeg², gik=abeg², i²k=ac⁶, jk=abc⁶, k²=c⁶, b²l=l, c²l=ac⁶, dl=al, el=ij, fl=gk, gl=abgj, hl=abc⁶, il=abij, jl=abc⁶, kl=c⁶, l²=c⁶, b²m=m, c²m=eg², dm=am, cem=abeg², e²m=bc⁶, efm=abeg², f²m=bc⁶, gm=gj, hm=c⁶, im=ij, jm=c⁶, km=abc⁶, lm=abc⁶, m²=c⁶, b²n=n, cn=abcm, dn=an, e²n=ac⁶, efn=eg², f²n=ac⁶, gn=abgj, hn=abc⁶, in=abij, jn=abc⁶, kn=c⁶, ln=c⁶, mn=abc⁶, n²=c⁶, b²o=o, c²o=eg², do=ao, eo=aben, fo=fm, go=gj, ho=c⁶, io=ij, jo=c⁶, ko=abc⁶, lo=abc⁶, mo=c⁶, no=abc⁶, o²=c⁶, b²p=p, c²p=bco, dp=ap, cep=aco, e³p=abc⁶, fp=abep, cgp=abeg², egp=bc⁶, g²p=ac⁶, hp=be²p, ip=gp, jp=abc⁶, kp=c⁶, lp=c⁶, mp=abc⁶, np=c⁶, op=abc⁶, p²=c⁶, b²q=q, cq=abcp, dq=aq, e²q=bgp, efq=agp, f²q=abe²p, gq=abgp, hq=ae²p, iq=abgp, jq=c⁶, kq=abc⁶, lq=abc⁶, mq=c⁶, nq=abc⁶, oq=c⁶, pq=abc⁶, q²=c⁶, b²r=r, cr=cp, dr=ar, e³r=abc⁶, efr=aco, f³r=c⁶, gr=ae²r, ehr=abeg², fhr=bc⁶, ir=ae²r, jr=abc⁶, kr=c⁶, lr=c⁶, mr=abc⁶, nr=c⁶, or=abc⁶, pr=c⁶, qr=abc⁶, r²=c⁶, b²s=s, c²s=bcp, ds=as, es=ap, fs=bp, gs=abeq, hs=abep, is=abeq, js=gp, ks=be²p, ls=abc⁶, ms=c⁶, ns=abc⁶, os=c⁶, ps=abc⁶, qs=c⁶, rs=abc⁶, s²=c⁶, b²t=t, ct=abcs, dt=at, e²t=aeq, eft=beq, f²t=bfq, gt=eq, ht=fq, it=eq, jt=abgp, kt=ae²p, lt=c⁶, mt=abc⁶, nt=c⁶, ot=abc⁶, pt=c⁶, qt=abc⁶, rt=c⁶, st=abc⁶, t²=c⁶, b²u=u, cu=cs, du=au, e²u=aer, efu=acp, f³u=bf²r, gu=er, hu=fr, iu=er, ju=ae²r, ku=hr, lu=abc⁶, mu=c⁶, nu=abc⁶, ou=c⁶, pu=abc⁶, qu=c⁶, ru=abc⁶, su=c⁶, tu=abc⁶, u²=c⁶, b²v=v, c²v=bcs, dv=av, cev=acs, e²v=p, fv=abev, gv=abet, hv=bp, iv=abet, jv=abeq, kv=abep, lv=gp, mv=be²p, nv=gp, ov=abc⁶, pv=c⁶, qv=abc⁶, rv=c⁶, sv=abc⁶, tv=c⁶, uv=abc⁶, v²=c⁶, b²w=w, cw=abcv, dw=aw, e²w=aet, efw=bet, f²w=bft, gw=et, hw=ft, iw=et, jw=eq, kw=fq, lw=abgp, mw=ae²p, nw=abgp, ow=c⁶, pw=abc⁶, qw=c⁶, rw=abc⁶, sw=c⁶, tw=abc⁶, uw=c⁶, vw=abc⁶, w²=c⁶, b²x=x, cx=cv, dx=ax, e²x=aeu, efx=acs, f²x=bfu, gx=eu, hx=fu, ix=eu, jx=er, kx=fr, lx=ae²r, mx=hr, nx=ae²r, ox=abc⁶, px=c⁶, qx=abc⁶, rx=c⁶, sx=abc⁶, tx=c⁶, ux=abc⁶, vx=c⁶, wx=abc⁶, x²=c⁶>

P = {a, b², abc, c², ac³, c⁴, ac⁵, c⁶, e², be³, e⁴, aef, abe³f, ae⁴f, f², af³, f⁴, aeg, fg, af²g, g², bh, eh, abfh, abgh, abei, ae²i, bfi, bgi, abhi, i², aj, bl, am, cm, bn, co, bp, abcp, ae²p, abeq, br, er, abhr, cs, et, abft, au, abeu, fu, af²u, abcv, ev, aw, abew, fw, bx, ex, abfx}

Phi = 1 a b a b c b d b ab² e f e g h i j k j l m n o p q r s t u v w x

Monoid Structure