Details Page for 0.7165

Complete Solution is Known:

MSV File: q-0.7165.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₃₁(0.7165):

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,y | 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, e³f=abe⁴, ef²=abe²f, f⁴=e⁴, b²g=g, c²g=ac⁴, dg=ag, ceg=bc⁴, e³g=abc⁶, efg=abe²g, f³g=c⁶, cg²=c⁵, e²g²=c⁶, fg²=ac⁶, g³=ac⁶, b²h=h, ch=abcg, dh=ah, e²h=be⁴, f²h=be⁴, gh=abg², h²=e⁴, b²i=i, ci=cg, di=ai, e²i=f²g, fi=abeg, egi=eg², g²i=abeg², ehi=ac⁶, i²=abhi, b²j=j, c²j=abc⁵, dj=aj, cej=c⁵, e²j=bc⁶, efj=abeg², f²j=bc⁶, cgj=bc⁶, egj=abeg², fgj=bc⁶, g²j=bc⁶, ehj=bc⁶, fhj=ac⁶, eij=ac⁶, gij=eg², hij=ac⁶, j²=hj, b²k=k, ck=abcj, dk=ak, e²k=ac⁶, efk=eg², f²k=ac⁶, egk=eg², fgk=ac⁶, g²k=ac⁶, ehk=ac⁶, fhk=bc⁶, eik=bc⁶, gik=abeg², hik=bc⁶, ejk=abeg², fjk=eg², gjk=eg², hjk=abeg², ijk=eg², k²=abhk, b²l=l, cl=cj, dl=al, e²l=bc⁶, efl=abeg², f²l=bc⁶, egl=abeg², fgl=bc⁶, g²l=bc⁶, hl=c⁶, eil=ac⁶, gil=eg², jl=hj, kl=hk, l²=c⁶, b²m=m, c²m=ac⁶, dm=am, em=il, fm=abgl, gm=abgl, hm=abc⁶, im=abil, jm=abhj, km=abhk, lm=abc⁶, m²=c⁶, b²n=n, cn=abcm, dn=an, en=abil, fn=gl, gn=gl, hn=c⁶, in=il, jn=hj, kn=hk, ln=c⁶, mn=abc⁶, n²=c⁶, b²o=o, co=cm, do=ao, eo=il, fo=abgl, go=abgl, ho=abc⁶, io=abil, jo=abhj, lo=abc⁶, mo=c⁶, no=abc⁶, o²=c⁶, b²p=p, c²p=eg², dp=ap, cep=abeg², e²p=bc⁶, efp=abeg², f²p=bc⁶, gp=gl, hp=c⁶, ip=il, cjp=ac⁶, ejp=bc⁶, fjp=ac⁶, kp=abko, lp=c⁶, mp=abc⁶, np=c⁶, op=abc⁶, p²=c⁶, b²q=q, cq=abcp, dq=aq, e²q=ac⁶, fq=abeq, gq=beg², hq=abc⁶, iq=beg², jq=aeg², kq=beg², lq=abc⁶, mq=c⁶, nq=abc⁶, oq=c⁶, pq=abc⁶, q²=c⁶, b²r=r, cr=cp, dr=ar, er=abeq, fr=eq, gr=aeg², hr=c⁶, ir=aeg², jr=beg², kr=aeg², lr=c⁶, mr=abc⁶, nr=c⁶, or=abc⁶, pr=c⁶, qr=abc⁶, r²=c⁶, b²s=s, c²s=bcp, ds=as, ces=acp, e³s=abc⁶, fs=abes, gs=abeq, hs=be²s, is=abeq, js=aeg², ks=c⁶, 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=abe²s, gt=eq, ht=ae²s, it=eq, jt=c⁶, kt=aeg², lt=c⁶, mt=abc⁶, nt=c⁶, ot=abc⁶, pt=c⁶, qt=abc⁶, rt=c⁶, st=abc⁶, t²=c⁶, b²u=u, cu=cs, du=au, eu=abet, fu=abft, gu=abeq, hu=be²s, iu=abeq, ju=aeg², ku=beg², 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=aes, fv=abev, gv=abet, hv=abes, iv=abet, jv=abeq, kv=eq, lv=abeq, mv=abc⁶, nv=c⁶, 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=abcp, lw=eq, mw=c⁶, nw=aeg², 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=bet, efx=aet, f²x=aft, gx=abet, hx=abft, ix=abet, jx=abcp, kx=cp, lx=abeq, mx=aeg², nx=beg², ox=abc⁶, px=c⁶, qx=abc⁶, rx=c⁶, sx=abc⁶, tx=c⁶, ux=abc⁶, vx=c⁶, wx=abc⁶, x²=c⁶, b²y=y, c²y=bcv, dy=ay, cey=acv, e²y=aev, fy=abey, cgy=acs, egy=bet, g²y=beq, hy=abev, iy=gy, jy=abet, ky=et, ly=abet, my=abeq, ny=eq, oy=abeq, py=abc⁶, qy=c⁶, ry=abc⁶, sy=c⁶, ty=abc⁶, uy=c⁶, vy=abc⁶, wy=c⁶, xy=abc⁶, y²=c⁶>

P = {a, b², abc, c², ac³, c⁴, ac⁵, c⁶, e², be³, e⁴, aef, f², af³, aeg, fg, af²g, g², bh, eh, abfh, abei, bgi, abhi, hj, abhk, ajk, al, bm, an, bo, cp, bq, bs, abcs, ae²s, abet, cv, abev, ew, abfw, ax, abex, fx, abcy, ey, abgy}

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

Monoid Structure