Details Page for 0.1005

Complete Solution is Known:

MSV File: q-0.1005.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₃₀(0.1005):

Q = <a,b,c,d,e,f,g,h,i,j,k | a²=1, b⁴=b², b²c⁴=b²c², bc⁵=bc³, c⁶=c⁴, bc²d=b³c³, c³d=b²c², b²d²=b², c²d²=b²c², bd³=bd, d⁴=d², b²e=ab², c²e=ac², bcde=ab³cd, bce²=abce, bde²=b³d, d²e²=b², be³=abe², ce³=ace², e⁴=ae³, b²f=b³c, c²f=bc³, bcd²f=bcf, d³f=df, bcef=ab²c², bd²ef=bef, be²f=b²c, ce²f=bc², de²f=b³cd, e³f=bce, bcf²=b³c³, bd²f²=bf², cd²f²=cf², e²f²=b²c², cf³=bf², bef⁴=bef², bf⁵=bf³, ef⁵=ef³, f⁶=f⁴, b²g=b³, bg²=b, cg²=c, dg²=d, e²g²=e², f³g²=f³, g³=g, b²h=ab²cd, c²h=ac⁴, bcdh=ab³c², d³h=dh, bceh=abch, de²h=ab²c, e³h=ae²h, bcfh=ab²c², bd²fh=bfh, befh=cd²eh, e²fh=bch, cf²h=bfh, g²h=h, bch²=abch, dh²=acd²h, beh²=abh², ceh²=ach², bfh²=b²c³, cfh²=bc⁴, f²h²=abdfh, h³=ae²h², b²i=b³, c²i=bc⁴, bcd²i=bci, d³i=di, bcei=ab²c, bdei=ab²d, be²i=b², de²i=b³d, e³i=ae²i, bcfi=b³c², bd²fi=bfi, cd²fi=cfi, befi=ab³c, d²efi=efi, e²fi=b²c, g²i=i, bchi=ab²c³, bd²hi=bhi, behi=b²cd, cehi=abch, ef³hi=cd²eh, bh²i=b²c², ch²i=abch, eh²i=abh², fh²i=acdfhi, bci²=b³c, cei²=cd²egi, e²i²=b², bf³i²=aef³i, ef³gi²=def⁴i², bhi²=ad²ehi, cd²hi²=chi², ehi²=acdegi, h²i²=acdhi², bd²i³=bi³, ei³=d²egi², d²f⁴i³=f⁴i³, f⁴gi³=df⁵i³, df³hi³=ef²i², f⁴hi³=def³i², bi⁴=bgi³, ci⁴=cgi³, di⁴=dgi³, fi⁴=fgi³, i⁵=gi⁴, b²j=ab³c, bcj=ab²c², c²j=abc³, bd²j=bj, d³j=dj, bej=b²c, cej=bc², e²j=bce, bfj=cd²j, cd²fj=cfj, defj=abef³, cf²j=cd²j, ef⁴j=ef²j, df⁵j=df³j, f²g²j=f²j, bhj=b²c³, chj=bc⁴, dfhj=abfh, h²j=bch, cdij=acdefgh, eij=b²c, cfij=acd²egh, bi²j=ab²c, df²i²j=abf²i², f⁴hi²j=aef²hj, ci³j=cgi²j, f⁴i³j=def⁴i², f³hi³j=aci²j, i⁴j=gi³j, j²=acdfj, b²c²k=ab³c³, e³k=ae²k, befk=cd²ek, cefk=abc²k, e²fk=abcek, bf²k=ab²c³, cf²k=ab³c², df²k=def³i², ef³k=b²c², f⁵k=f³k, ef²gk=b²c³, f⁴gk=f²gk, f²g²k=f⁴k, cdhk=b³c³, cehk=achk, dehk=acd²ek, be²hk=abehk, bfhk=b³c², cfhk=abc⁴k, dfhk=b²c³, efhk=abchk, f⁴hk=f²hk, eh²k=ah²k, fh²k=abchk, cdeik=ab³cdk, ce²ik=aceik, cfik=ab³c³, f²ik=def⁴i², bfgik=aefik, efgik=abfik, bhik=abcdik, chik=bchk, dhik=acd²ik, e²hik=aehik, fhik=b³c², h²ik=bh²k, ci²k=aefik, bdi²k=adeik, dei²k=degik, bfi²k=aefik, d²fi²k=fi²k, efi²k=abfik, bi³k=ad²egik, di³k=dgi²k, fi³k=fgi²k, i⁴k=d²i²k, cjk=abc²k, dejk=acd³egk, dfjk=abcdfk, efjk=aef²k, f²jk=b²c², fgjk=abcfgk, hjk=abchk, bijk=cd²egk, d²ijk=ijk, fijk=b²c³, i²jk=abfik, b²k²=b²c², bc³k²=b³c³, c⁴k²=b²c², c²dk²=c³k², bdek²=bcfk, cd²ek²=ab²c³, ce²k²=acek², cfk²=bc²k², bdfk²=abcdfgk, defk²=ab³c², f³k²=b³c³, f²gk²=b³c², chk²=ac³k², dhk²=acd²k², behk²=bc²k², e²hk²=aehk², fhk²=ab³c³, h²k²=b²c², bcik²=abcfgk, cdik²=acdfgk, ceik²=ab³c³, deik²=cef²i, e²ik²=bc²k², fik²=bfk², ehik²=b³c², hi²k²=beik², bjk²=ab²c³, djk²=abcdk², egjk²=aefgk², ijk²=bcfgk, bck³=abc²gk², c³k³=abc²k², bdk³=ab²c², d²k³=abcd²k², cdek³=acdk³, be²k³=abek³, de²k³=adek³, bfk³=bei²k², dfk³=ab²c³, f²k³=ab³c³, cdgk³=abek³, begk³=acdk³, g²k³=k³, hk³=acdk³, bik³=ab³c³, cik³=begi²k², dik³=bcdfgk, eik³=b²c³, i²k³=ab³c³, ejk³=aefk³, fjk³=b³c³, bk⁴=b³c², ck⁴=b²c³, dk⁴=b²c³, ek⁴=begi²k², fk⁴=b³c³, ik⁴=abei²k², jk⁴=ab³c³, k⁵=ab³c³>

P = {a, b², c², b²c², c⁴, ad, bcd, b³cd, ad², ad³, de, d³e, e², ae³, af, bcf, adf, ad²f, ef, d²ef, af², adf², ad²f², def², af³, adf³, ad²f³, ef³, def³, d²ef³, af⁴, adf⁴, ad²f⁴, def⁴, af⁵, adf⁵, ad²f⁵, ag, bcg, bc³g, adg, ad²g, ad³g, eg, abceg, deg, d²eg, d³eg, ade³g, afg, adfg, ad²fg, efg, defg, d²efg, af²g, adf²g, ad²f²g, ef²g, def²g, d²ef²g, af³g, adf³g, ad²f³g, ef³g, d²ef³g, af⁴g, adf⁴g, ad²f⁴g, ef⁴g, def⁴g, d²ef⁴g, af⁵g, adf⁵g, ad²f⁵g, ag², afg², efg², af²g², abh, acdh, abd²h, beh, cdeh, bd²eh, abe²h, abdfh, f³h, abdf³h, aef³h, f⁵h, ae²gh, fgh, d²fgh, aefgh, ad²efgh, f²gh, d²f²gh, aef²gh, ad²ef²gh, f³gh, d²f³gh, aef³gh, ad²ef³gh, f⁴gh, d²f⁴gh, aef⁴gh, ad²ef⁴gh, f⁵gh, d²f⁵gh, h², aeh², e²h², bgh², ai, adi, ad²i, abei, acdei, afi, adfi, ad²fi, acefi, af²i, adf²i, ad²f²i, af³i, adf³i, ad²f³i, af⁴i, adf⁴i, ad²f⁴i, af⁵i, adf⁵i, ad²f⁵i, agi, adgi, bcdgi, ad²gi, acegi, ce²gi, afgi, adfgi, ad²fgi, af²gi, adf²gi, ad²f²gi, def²gi, af³gi, adf³gi, ad²f³gi, af⁴gi, adf⁴gi, ad²f⁴gi, af⁵gi, adf⁵gi, ad²f⁵gi, ehi, d²ehi, ae²hi, fhi, d²fhi, defhi, f²hi, d²f²hi, f³hi, d²f³hi, f⁴hi, d²f⁴hi, f⁵hi, d²f⁵hi, abghi, acdghi, abdfghi, f³ghi, abdf³ghi, f⁵ghi, gh²i, ai², adi², ad²i², afi², adfi², ad²fi², af²i², adf²i², ad²f²i², def²i², af³i², adf³i², ad²f³i², af⁴i², adf⁴i², ad²f⁴i², af⁵i², adf⁵i², ad²f⁵i², agi², adgi², ad²gi², abegi², afgi², adfgi², ad²fgi², af²gi², adf²gi², ad²f²gi², af³gi², adf³gi², ad²f³gi², af⁴gi², adf⁴gi², ad²f⁴gi², af⁵gi², adf⁵gi², ad²f⁵gi², acdhi², f³hi², f⁵hi², fghi², d²fghi², f²ghi², d²f²ghi², f³ghi², d²f³ghi², f⁴ghi², d²f⁴ghi², f⁵ghi², d²f⁵ghi², ai³, adi³, ad²i³, afi³, adfi³, ad²fi³, af²i³, adf²i³, ad²f²i³, af³i³, adf³i³, ad²f³i³, af⁴i³, adf⁴i³, af⁵i³, adf⁵i³, agi³, adgi³, ad²gi³, afgi³, adfgi³, ad²fgi³, af²gi³, adf²gi³, ad²f²gi³, af³gi³, adf³gi³, ad²f³gi³, fhi³, d²fhi³, f²hi³, d²f²hi³, f³hi³, acdghi³, f³ghi³, ai⁴, agi⁴, acdfj, abdgj, acd²gj, fhj, aefhj, dghj, adeghj, ij, dij, d²ij, fij, d²fij, f²ij, d²f²ij, f³ij, d²f³ij, f⁴ij, d²f⁴ij, f⁵ij, fghij, gi²j, fhi²j, dghi²j, i³j, dhi³j, fghi³j, dek, d³ek, acdfk, efk, d²efk, abdgk, ac²dgk, abd²gk, bdegk, cd²egk, abfgk, abdfgk, abd²fgk, efg²k, bchk, fhk, cghk, dghk, acgh²k, acik, abdik, acd²ik, abfik, degik, jk, d²jk, aejk, gjk, g²jk, aeg²jk, gijk, k², c²k², cdk², d²k², cd³k², acdek², e²k², efk², f²k², bcgk², bcdgk², egk², abcegk², g²k², ahk², ehk², abdik², abeik², agik², d²gik², i²k², d²i²k², egi²k², agi³k², efk³, c²gk³, adgk³, egk³, degk³, fgk³, aik³, jk³, k⁴}

Phi = 1 a 1 1 a 1 a 1 b a b b b b a 1 c c c a d c e f e g b h i j k

Monoid Structure