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 Q₃₈(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,z,A,B,C,D | a²=1, b³=b, b²c=c, c⁹=ac⁸, bd=ab, cd=ac, d²=b², b²e=e, c²e=abc³, de=ae, ce²=c³, e⁷=bc⁸, b²f=f, cf=abce, df=af, e³f=abe⁴, ef²=abe²f, f⁷=ac⁸, b²g=g, c²g=ac⁴, dg=ag, ceg=bc⁴, e⁵g=abc⁸, efg=abe²g, f³g=abe³g, cg²=c⁵, e²g²=ae⁴g, fg²=be³g, g³=e⁴g, b²h=h, ch=abcg, dh=ah, e²h=be⁴, f²h=bf⁴, gh=abg², h²=f⁴, b²i=i, ci=cg, di=ai, e²i=f²g, fi=abeg, egi=eg², ehi=be³g, i²=abhi, b²j=j, c²j=abc⁵, dj=aj, cej=c⁵, e⁴j=bc⁸, e²fj=abe³j, f²j=e²j, cgj=bc⁶, e²gj=abc⁸, fgj=be³j, g²j=bc⁸, ehj=be³j, fhj=ae³j, eij=ae³j, hij=ac⁸, cj²=c⁷, ej²=bc⁸, fj²=ac⁸, gj²=ac⁸, hj²=bc⁸, ij²=ac⁸, j³=bc⁸, b²k=k, ck=abcj, dk=ak, e⁵k=abc⁸, e²fk=abe³k, f²k=e²k, e²gk=ae⁴k, fgk=be³k, g²k=e⁴k, ehk=be³k, fhk=ae³k, eik=ae³k, hik=abe⁴k, ejk=gik, fjk=abgik, gjk=gij, hjk=abgij, ijk=gij, j²k=abgij, ek²=abe⁴k, fk²=e⁴k, gk²=ac⁸, hk²=bc⁸, ik²=ac⁸, jk²=gij, k³=ac⁸, b²l=l, cl=cj, dl=al, e²l=ae³g, efl=abeg², f²l=ae³g, egl=g²i, fgl=abe⁴g, g²l=bc⁸, hl=abe³g, eil=e⁴g, gil=gij, jl=j², kl=abk², l²=ae⁴g, b²m=m, c²m=ac⁶, dm=am, cem=bc⁶, e²m=ae³j, efm=abegj, f²m=ae³j, cgm=c⁷, egm=gij, fgm=ac⁸, g²m=ac⁸, hm=abe³j, eim=bc⁸, gim=abgij, cjm=bc⁸, ejm=ac⁸, fjm=bc⁸, gjm=bc⁸, ijm=bc⁸, j²m=ac⁸, ekm=bc⁸, fkm=ac⁸, gkm=ac⁸, ikm=ac⁸, jkm=gij, k²m=ac⁸, lm=abc⁸, m²=c⁸, b²n=n, cn=abcm, dn=an, e²n=ae³k, efn=abegk, f²n=ae³k, egn=gik, fgn=abe⁴k, g²n=bc⁸, hn=abe³k, ein=e⁴k, gin=gij, ejn=bc⁸, fjn=ac⁸, gjn=ac⁸, ijn=ac⁸, j²n=bc⁸, kn=abkm, ln=ae⁴k, mn=abc⁸, n²=c⁸, b²o=o, co=cm, do=ao, eo=il, fo=abgl, g²o=ac⁸, ho=be⁴g, gio=abgij, jo=jm, gko=ac⁸, iko=ac⁸, k²o=ac⁸, lo=abc⁸, mo=c⁸, no=abc⁸, o²=c⁸, b²p=p, c³p=abc⁸, dp=ap, cep=abc²p, e²p=bc⁸, efp=abgij, f²p=bc⁸, cgp=bc⁸, egp=abgij, fgp=bc⁸, g²p=bc⁸, hp=c⁸, eip=ac⁸, gip=gij, cjp=ac⁸, ejp=bc⁸, fjp=ac⁸, gjp=ac⁸, ijp=ac⁸, j²p=bc⁸, ekp=ac⁸, fkp=bc⁸, gkp=bc⁸, ikp=bc⁸, jkp=abgij, k²p=bc⁸, lp=c⁸, mp=abc⁸, np=c⁸, op=abc⁸, p²=c⁸, b²q=q, cq=abcp, dq=aq, e²q=e⁴k, fq=abeq, gq=agik, hq=be⁴k, iq=agik, jq=agij, kq=bgij, lq=abc⁸, mq=c⁸, nq=abc⁸, oq=c⁸, pq=abc⁸, q²=c⁸, b²r=r, cr=cp, dr=ar, e²r=bc⁸, fr=aber, gr=agij, hr=c⁸, ir=agij, jr=bgij, kr=agij, lr=c⁸, mr=abc⁸, nr=c⁸, or=abc⁸, pr=c⁸, qr=abc⁸, r²=c⁸, b²s=s, c³s=bgij, ds=as, ces=abc²s, e³s=abc⁸, fs=abes, cgs=abgij, egs=bc⁸, g²s=ac⁸, hs=be²s, is=gs, js=agij, ks=c⁸, ls=abc⁸, ms=c⁸, ns=abc⁸, os=c⁸, ps=abc⁸, qs=c⁸, rs=abc⁸, s²=c⁸, b²t=t, ct=abcs, dt=at, e²t=bgs, eft=ags, f²t=abe²s, gt=abgs, ht=ae²s, it=abgs, jt=c⁸, kt=agij, lt=c⁸, mt=abc⁸, nt=c⁸, ot=abc⁸, pt=c⁸, qt=abc⁸, rt=c⁸, st=abc⁸, t²=c⁸, b²u=u, cu=cs, du=au, e²u=ags, efu=bgs, f²u=e²s, gu=gs, hu=be²s, iu=gs, ju=agij, ku=bgij, lu=abc⁸, mu=c⁸, nu=abc⁸, ou=c⁸, pu=abc⁸, qu=c⁸, ru=abc⁸, su=c⁸, tu=abc⁸, u²=c⁸, b²v=v, c³v=bc²s, dv=av, cev=abc²v, e²v=aes, fv=abev, gv=eu, hv=abes, iv=eu, jv=gs, kv=abgs, lv=gs, mv=abc⁸, nv=c⁸, ov=abc⁸, pv=c⁸, qv=abc⁸, rv=c⁸, sv=abc⁸, tv=c⁸, uv=abc⁸, v²=c⁸, b²w=w, cw=abcv, dw=aw, e²w=beu, efw=aeu, f²w=afu, gw=abeu, hw=abfu, iw=abeu, jw=abgs, kw=ac²s, lw=abgs, mw=c⁸, nw=agij, ow=c⁸, pw=abc⁸, qw=c⁸, rw=abc⁸, sw=c⁸, tw=abc⁸, uw=c⁸, vw=abc⁸, w²=c⁸, b²x=x, cx=cv, dx=ax, e²x=aeu, efx=beu, f²x=bfu, gx=eu, hx=fu, ix=eu, jx=ac²s, kx=bc²s, lx=gs, mx=agij, nx=bgij, ox=abc⁸, px=c⁸, qx=abc⁸, rx=c⁸, sx=abc⁸, tx=c⁸, ux=abc⁸, vx=c⁸, wx=abc⁸, x²=c⁸, b²y=y, c²y=bcv, dy=ay, cey=acv, e²y=aev, fy=abey, cgy=abc²v, egy=aeu, g²y=ags, hy=abev, iy=gy, jy=eu, ky=abeu, ly=eu, my=gs, ny=abgs, oy=gs, py=abc⁸, qy=c⁸, ry=abc⁸, sy=c⁸, ty=abc⁸, uy=c⁸, vy=abc⁸, wy=c⁸, xy=abc⁸, y²=c⁸, b²z=z, cz=abcy, dz=az, e²z=aew, efz=bew, f²z=bfw, gz=ew, hz=fw, iz=ew, jz=abeu, kz=ac²v, lz=abeu, mz=abgs, nz=ac²s, oz=abgs, pz=c⁸, qz=agij, rz=c⁸, sz=abc⁸, tz=c⁸, uz=abc⁸, vz=c⁸, wz=abc⁸, xz=c⁸, yz=abc⁸, z²=c⁸, b²A=A, c²A=bcy, dA=aA, ceA=acy, e²A=aey, fA=abeA, cgA=acv, egA=agy, g²A=aeu, hA=abey, iA=gA, jA=gy, kA=abgy, lA=gy, mA=eu, nA=abeu, oA=eu, pA=gs, qA=abgs, rA=gs, sA=abc⁸, tA=c⁸, uA=abc⁸, vA=c⁸, wA=abc⁸, xA=c⁸, yA=abc⁸, zA=c⁸, A²=c⁸, b²B=B, cB=cA, dB=aB, e³B=ex, efB=abe²B, f²B=x, gB=ae²B, hB=bx, iB=ae²B, jB=abcv, kB=cv, lB=ex, mB=ac²v, nB=bc²v, oB=eu, pB=ac²s, qB=bc²s, rB=gs, sB=agij, tB=bgij, uB=abc⁸, vB=c⁸, wB=abc⁸, xB=c⁸, yB=abc⁸, zB=c⁸, AB=c⁸, B²=c⁸, b²C=C, c²C=bcA, dC=aC, ceC=acA, e²C=aeA, fC=abeC, cgC=acy, egC=agA, g²C=agy, hC=abeA, iC=gC, jC=gA, kC=abgA, lC=gA, mC=gy, nC=abgy, oC=gy, pC=eu, qC=abeu, rC=eu, sC=gs, tC=abgs, uC=gs, vC=abc⁸, wC=c⁸, xC=abc⁸, yC=c⁸, zC=abc⁸, AC=abc⁸, BC=abc⁸, C²=c⁸, b²D=D, cD=abcC, dD=aD, e³D=ez, efD=abe²D, f²D=z, gD=ae²D, hD=bz, iD=ae²D, jD=ez, kD=abcy, lD=ez, mD=ew, nD=abcv, oD=ew, pD=abeu, qD=ac²v, rD=abeu, sD=abgs, tD=ac²s, uD=abgs, vD=c⁸, wD=agij, xD=c⁸, yD=abc⁸, zD=c⁸, AD=c⁸, BD=c⁸, CD=abc⁸, D²=c⁸>

P = {a, b², abc, c², ac³, c⁴, ac⁵, c⁶, ac⁷, c⁸, e², be³, e⁴, be⁵, e⁶, aef, f², af³, f⁴, af⁵, f⁶, aeg, abe³g, ae⁴g, fg, af²g, g², bh, eh, abfh, abei, bgi, abhi, be²j, e³j, hj, j², ae²k, abe³k, ae⁴k, abhk, ajk, k², al, bm, abjm, km, an, jn, bo, cp, bq, bs, abcs, bc²s, ae²s, abet, eu, cv, ac²v, abev, ew, abfw, ax, abex, fx, abcy, ey, abgy, az, abez, fz, cA, abeA, gA, abeB, ae²B, fB, bC, abcC, eC, abgC, aD, abeD, ae²D, fD}

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 z bfB A bfD B C D

Monoid Structure