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 Q₄₁(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,E | a²=1, b³=b, b²c=c, c¹⁰=ac⁹, bd=ab, cd=ac, d²=b², b²e=e, c²e=abc³, de=ae, ce²=c³, e⁸=ac⁹, b²f=f, cf=abce, df=af, e³f=abe⁴, ef²=abe²f, f⁸=ac⁹, b²g=g, c²g=ac⁴, dg=ag, ceg=bc⁴, e⁶g=c⁹, 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, e⁵j=ac⁹, e²fj=abe³j, f²j=e²j, cgj=bc⁶, e²gj=ae⁴j, fgj=be³j, g²j=e⁴j, ehj=be³j, fhj=ae³j, eij=ae³j, hij=abe⁴j, cj²=c⁷, ej²=e⁴j, fj²=abe⁴j, gj²=c⁹, hj²=abc⁹, ij²=c⁹, j³=abc⁹, b²k=k, ck=abcj, dk=ak, e⁶k=c⁹, e²fk=abe³k, f²k=e²k, e²gk=ae⁴k, fgk=be³k, g²k=e⁴k, ehk=be³k, fhk=ae³k, eik=ae³k, hik=abe⁴k, ejk=gik, fjk=abgik, hjk=abgjk, ijk=gjk, ek²=abe⁴k, fk²=e⁴k, gk²=be⁵k, hk²=ae⁵k, ik²=be⁵k, jk²=abj²k, k³=c⁹, b²l=l, cl=cj, dl=al, e²l=ae³g, efl=abeg², f²l=ae³g, egl=g²i, fgl=abe⁴g, g²l=ae⁵g, hl=abe³g, eil=e⁴g, 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=abe⁴j, g²m=c⁹, hm=abe³j, eim=e⁴j, gim=j²k, cjm=bc⁸, ejm=c⁹, fjm=abc⁹, gjm=abc⁹, ijm=abc⁹, j²m=c⁹, ekm=ae⁵k, fkm=be⁵k, gkm=c⁹, ikm=c⁹, jkm=abj²k, k²m=c⁹, lm=ae⁴j, m²=ac⁹, b²n=n, cn=abcm, dn=an, e²n=ae³k, efn=abegk, f²n=ae³k, egn=gik, fgn=abe⁴k, g²n=ae⁵k, hn=abe³k, ein=e⁴k, gin=gjk, ejn=ae⁵k, fjn=be⁵k, gjn=c⁹, ijn=c⁹, j²n=abc⁹, kn=abkm, ln=ae⁴k, mn=e⁵k, n²=abe⁵k, b²o=o, co=cm, do=ao, eo=il, fo=abgl, g²o=c⁹, ho=be⁴g, gio=j²k, jo=jm, gko=c⁹, iko=c⁹, k²o=c⁹, lo=e⁵g, mo=ac⁹, no=e⁵k, o²=ac⁹, b²p=p, c³p=abc⁸, dp=ap, cep=abc²p, e²p=e⁴j, efp=abgij, f²p=e⁴j, cgp=bc⁸, egp=j²k, fgp=abc⁹, g²p=abc⁹, hp=be⁴j, eip=c⁹, gip=abj²k, cjp=c⁹, ejp=abc⁹, fjp=c⁹, gjp=c⁹, ijp=c⁹, j²p=abc⁹, ekp=c⁹, fkp=abc⁹, gkp=abc⁹, ikp=abc⁹, jkp=j²k, k²p=abc⁹, lp=ac⁹, mp=bc⁹, np=ac⁹, op=bc⁹, p²=ac⁹, b²q=q, cq=abcp, dq=aq, e²q=e⁴k, fq=abeq, gq=agik, hq=be⁴k, iq=agik, jq=agjk, kq=bgjk, lq=e⁵k, mq=ac⁹, nq=bc⁹, oq=ac⁹, pq=bc⁹, q²=ac⁹, b²r=r, cr=cp, dr=ar, e²r=ae⁵g, fr=aber, gr=agil, hr=abe⁵g, ir=agil, jr=aj²k, kr=agjk, lr=ac⁹, mr=bc⁹, nr=ac⁹, or=bc⁹, pr=ac⁹, qr=bc⁹, r²=ac⁹, b²s=s, c³s=aj²k, ds=as, ces=abc²s, e³s=bc⁹, fs=abes, cgs=j²k, egs=abc⁹, g²s=c⁹, hs=be²s, is=gs, js=bj²k, ks=ac⁹, ls=bc⁹, ms=ac⁹, ns=bc⁹, os=ac⁹, ps=bc⁹, qs=ac⁹, rs=bc⁹, s²=ac⁹, b²t=t, ct=abcs, dt=at, e³t=ac⁹, eft=abe²t, f³t=bc⁹, gt=ae²t, ht=bf²t, it=ae²t, jt=ac⁹, kt=bj²k, lt=ac⁹, mt=bc⁹, nt=ac⁹, ot=bc⁹, pt=ac⁹, qt=bc⁹, rt=ac⁹, st=bc⁹, t²=ac⁹, b²u=u, cu=cs, du=au, e²u=ags, efu=bgs, f²u=e²s, gu=gs, hu=be²s, iu=gs, ju=bj²k, ku=aj²k, lu=bc⁹, mu=ac⁹, nu=bc⁹, ou=ac⁹, pu=bc⁹, qu=ac⁹, ru=bc⁹, su=ac⁹, tu=bc⁹, u²=ac⁹, b²v=v, c⁴v=abj²k, dv=av, cev=abc²v, e³v=ae²s, fv=abev, cgv=ac³v, egv=ags, g²v=abc⁹, hv=be²v, iv=gv, jv=gs, kv=abgs, lv=gs, mv=bc⁹, nv=ac⁹, ov=bc⁹, pv=ac⁹, qv=bc⁹, rv=ac⁹, sv=bc⁹, tv=ac⁹, uv=bc⁹, v²=ac⁹, b²w=w, cw=abcv, dw=aw, e²w=bgv, efw=agv, f³w=ae²s, gw=abgv, hw=bf²w, iw=abgv, jw=abgs, kw=abc³v, lw=abgs, mw=ac⁹, nw=bj²k, ow=ac⁹, pw=bc⁹, qw=ac⁹, rw=bc⁹, sw=ac⁹, tw=bc⁹, uw=ac⁹, vw=bc⁹, w²=ac⁹, b²x=x, cx=cv, dx=ax, e²x=agv, efx=bgv, f²x=abf²w, gx=gv, hx=af²w, ix=gv, jx=abc³v, kx=c³v, lx=gs, mx=bj²k, nx=aj²k, ox=bc⁹, px=ac⁹, qx=bc⁹, rx=ac⁹, sx=bc⁹, tx=ac⁹, ux=bc⁹, vx=ac⁹, wx=bc⁹, x²=ac⁹, b²y=y, c³y=bc²v, dy=ay, cey=abc²y, e²y=aev, fy=abey, cgy=abc²v, egy=agv, g²y=ags, hy=abev, iy=gy, jy=gv, ky=abgv, ly=gv, my=gs, ny=abgs, oy=gs, py=bc⁹, qy=ac⁹, ry=bc⁹, sy=ac⁹, ty=bc⁹, uy=ac⁹, vy=bc⁹, wy=ac⁹, xy=bc⁹, y²=ac⁹, b²z=z, cz=abcy, dz=az, e³z=abgv, efz=abe²z, f³z=bf²w, gz=ae²z, hz=bf²z, iz=ae²z, jz=abgv, kz=ac²v, lz=abgv, mz=abgs, nz=abc³v, oz=abgs, pz=ac⁹, qz=bj²k, rz=ac⁹, sz=bc⁹, tz=ac⁹, uz=bc⁹, vz=ac⁹, wz=bc⁹, xz=ac⁹, yz=bc⁹, z²=ac⁹, b²A=A, c²A=bcy, dA=aA, ceA=acy, e²A=aey, fA=abeA, cgA=abc²y, egA=agy, g²A=agv, hA=abey, iA=gA, jA=gy, kA=abgy, lA=gy, mA=gv, nA=abgv, oA=gv, pA=gs, qA=abgs, rA=gs, sA=bc⁹, tA=ac⁹, uA=bc⁹, vA=ac⁹, wA=bc⁹, xA=ac⁹, yA=bc⁹, zA=ac⁹, A²=ac⁹, b²B=B, cB=cA, dB=aB, e³B=ex, efB=abe²B, f³B=fx, gB=ae²B, hB=bf²B, iB=ae²B, jB=ac²y, kB=bc²y, lB=ex, mB=ac²v, nB=bc²v, oB=gv, pB=abc³v, qB=c³v, rB=gs, sB=bj²k, tB=aj²k, uB=bc⁹, vB=ac⁹, wB=bc⁹, xB=ac⁹, yB=bc⁹, zB=ac⁹, AB=ac⁹, B²=ac⁹, b²C=C, c²C=bcA, dC=aC, ceC=acA, e²C=aeB, efC=beB, f²C=bfB, gC=eB, hC=fB, iC=eB, jC=abcy, kC=cy, lC=ae²B, mC=ac²y, nC=bc²y, oC=ex, pC=ac²v, qC=bc²v, rC=gv, sC=abc³v, tC=c³v, uC=gs, vC=bj²k, wC=aj²k, xC=bc⁹, yC=ac⁹, zC=bc⁹, AC=bc⁹, BC=bc⁹, C²=ac⁹, b²D=D, c²D=bcC, dD=aD, ceD=acC, e³D=eA, fD=abeD, cgD=acA, e²gD=gA, g²D=agA, hD=be²D, iD=gD, jD=aegD, kD=begD, lD=aegD, mD=gA, nD=abgA, oD=gA, pD=gy, qD=abgy, rD=gy, sD=gv, tD=abgv, uD=gv, vD=gs, wD=abgs, xD=gs, yD=bc⁹, zD=ac⁹, AD=ac⁹, BD=ac⁹, CD=bc⁹, D²=ac⁹, b²E=E, cE=abcD, dE=aE, e⁴E=aez, efE=abe²E, f⁴E=bfz, gE=ae²E, hE=bf²E, iE=ae²E, jE=e³E, kE=abcA, lE=e³E, mE=ez, nE=abcy, oE=ez, pE=ae²z, qE=ac²y, rE=ae²z, sE=abgv, tE=ac²v, uE=abgv, vE=abgs, wE=abc³v, xE=abgs, yE=ac⁹, zE=bj²k, AE=bc⁹, BE=bc⁹, CE=ac⁹, DE=bc⁹, E²=ac⁹>

P = {a, b², abc, c², ac³, c⁴, ac⁵, c⁶, ac⁷, c⁸, ac⁹, e², be³, e⁴, be⁵, e⁶, be⁷, aef, f², af³, f⁴, af⁵, f⁶, af⁷, aeg, abe³g, ae⁴g, abe⁵g, fg, af²g, g², bh, eh, abfh, abei, bgi, abhi, be²j, e³j, be⁴j, hj, j², ae²k, abe³k, ae⁴k, abe⁵k, abhk, ajk, k², al, bm, abjm, km, an, jn, bo, cp, bq, bs, abcs, bc²s, ae²s, abet, bf²t, eu, cv, ac²v, c³v, abev, gv, ew, abfw, ax, abex, fx, abcy, bc²y, ey, abgy, az, abez, ae²z, fz, af²z, cA, abeA, gA, abeB, ae²B, fB, af²B, bC, abcC, eC, abfC, aD, cD, abeD, ae²D, gD, begD, bE, eE, be²E, e³E, abfE, bf²E, abf³E}

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 f²E B aeD bfE C D E

Monoid Structure