Details Page for 0.1602

Complete Solution is Known:

MSV File: q-0.1602.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₈(0.1602):

Q = <a,b,c,d,e,f,g,h,i,j | a²=1, b⁴=b², b³c³=bc³, c⁴=b²c², b²d=b³, bc³d=b²c³, bc²d²=bc², c³d²=c³, bd³=bd, cd³=cd, d⁴=d², b²e=e, de=be, c²e²=e², e⁴=ae³, bcf=bc², c²f=c³, ef=ce, bdf³=b²f³, cdf³=b³c², bf⁴=b³c², cf⁴=b²c³, df⁴=b³c², f⁵=b²c³, b²c²g=b²c², bc³g=bc³, bd²g=bg, d³g=dg, eg=e, bf²g=b³c², cf²g=b²c³, d²f²g=f²g, f³g=b²c³, bc²g²=bc²g, c³g²=c³g, bg³=bg², cg³=cg², f²g³=f²g², g⁴=g³, bc²h=ab³c², c³h=ab²c³, eh=ae, b²fh=b²ch, cfh=c²h, bf²h=ab³c², d³f²h=df²h, f³h=ab²c³, b³gh=bgh, bcgh=ab³cg², bdgh=b²gh, bfgh=ab³cg², f²gh=ab²c², bg²h=bgh, c²g²h=c²gh, g³h=g²h, b³h²=bh², c²h²=b²c², bdh²=b²h², d³h²=dh², bfh²=bch², d²fh²=fh², f²h²=b²c², bgh²=abgh, cgh²=b²cg², dgh²=abgh, fgh²=b²cg², g²h²=gh², bh³=abh², ch³=ab²ch², dh³=abh², fh³=ab²ch², gh³=agh², h⁴=ah³, b²c³i=c³i, c³di=bc³i, e²i=ce², cdf²i=bc³i, f⁴i=cf³i, bc²gi=bc²i, c³gi=c³i, cfgi=c²gi, f²gi=b²c²i, c²g²i=c²gi, cg²hi=cghi, bc²i²=bc²g, c³i²=b²c³, ei²=e, bf²i²=bf², cf³i²=cf³, d²f³i²=d²f³, b²gi²=b²g², bcgi²=bcg², bfgi²=bfg², bg²i²=bgi², g³i²=g²i², bfhi²=bchi², bghi²=bgh, cghi²=cg²h, fghi²=fgh, bh²i²=bh², ch²i²=fh², fh²i²=fh², gh²i²=gh², h³i²=h³, cf²i³=cf²i, f³i³=f³i, bgi³=bg²i, c²gi³=c²gi, g²i³=g³i, b²hi⁴=ab²h², bdhi⁴=ad²h²i², h²i⁴=h²i², f²i⁵=f²i³, bi⁶=bi⁴, i⁷=i⁵, e³j=be³, bf²j=b³c²j, cf²j=b²c³j, d³f²j=df²j, df³j=bc³j, f⁴j=b²c²j, bc²gj=b³c²j, c³gj=b²c³j, b³fgj=bfgj, cfgj=c²gj, bdfgj=b²fgj, b³c²ij=bc²ij, bc²dij=b²c²ij, cfij=c²ij, f³i²j=f³j, b²c²j²=b²c², bc³j²=bc³, ej²=e, bd²fj²=bfj², f³j²=b²c³, b³cgj²=bcgj², bcdgj²=b²cgj², c²d²gj²=c²gj², bfgj²=bcgj², f²gj²=c²gj², c²g²j²=b²c², bfhj²=b³chj², bghj²=ab³g²j², c²ghj²=ab²c², fghj²=ab²cg²j², cg²hj²=afg³j², bh²j²=b³g²j², fh²j²=b²cg²j², gh²j²=b²g²j², bc²ij²=b³c²i, c³ij²=c³i, b³fij²=bfij², bdfij²=b²fij², b³gij²=bgij², c²gij²=b²c²i, bdgij²=b²gij², cghij²=afg³ij², b³i²j²=bi²j², bdi²j²=b²i²j², bfi²j²=bci²j², bgi²j²=b³g²j², cg²i²j²=cg²j², fg²i²j²=fg³j², h²i²j²=ah³j², f²i³j²=b²c²i, bhi³j²=abgij², d³i⁴j²=di⁴j², bg²j³=abghj, cg²j³=b²cg²j, fg²j³=b²cg²j, f²hj³=c²hj³, g²hj³=b²ghj, ch²j³=acghj³, h³j³=b²ghj, b³ij³=bij³, bdij³=b²ij³, bgij³=abghij, fgij³=cgij³, g³ij³=g²ij³, bhij³=bghij, h²ij³=ab²ghij, bi²j³=ab³hj³, c²i²j³=b²c²j, d³i²j³=di²j³, f²i²j³=b²c²j, g²i²j³=g³j³, fhi²j³=cghj³, ghi²j³=b²ghj, chi³j³=acgi³j³, bc²j⁴=adf²hi²j², c³j⁴=cd²f², bd²j⁴=bj⁴, fgj⁴=cgj⁴, d²g²j⁴=g²j⁴, g³j⁴=b²g²j², bhj⁴=ab³g²j², c²hj⁴=f²hi²j², ghj⁴=ag²j⁴, h²j⁴=b²g²j², d³ij⁴=dij⁴, f²ij⁴=b²c²i, cgij⁴=ch²ij², g²ij⁴=b²g²ij², chij⁴=ach²ij², fhij⁴=ach²ij², ci²j⁴=b²cg²j², fi²j⁴=b²cg²j², hi²j⁴=ab²g²j², d³j⁵=dj⁵, b³fj⁵=bfj⁵, cfj⁵=c²j⁵, bdfj⁵=b²fj⁵, d²f²j⁵=f²j⁵, b²gj⁵=ab²hj³, bcgj⁵=ab³chj³, d²gj⁵=gj⁵, chj⁵=cghj³, fhj⁵=cghj³, bcij⁵=b³cgij, c²ij⁵=ac²hij³, bfij⁵=b³cgij, gij⁵=ad²ghij³, dhij⁵=bghij, i²j⁵=ab²ghj, b³cj⁶=bcj⁶, bcdj⁶=b²cj⁶, cd²j⁶=cj⁶, bfj⁶=bcj⁶, d²fj⁶=fj⁶, f²j⁶=c²j⁶, cgj⁶=b²cg²j², g²j⁶=bdgj⁶, d²hj⁶=hj⁶, bij⁶=bgij², fij⁶=b²cgij², hij⁶=ab²g²ij², d²j⁷=j⁷, fj⁷=cj⁷, bgj⁷=abghj, hj⁷=agj⁷, cij⁷=b²cg²ij, c²j⁸=c²j⁶, j⁹=j⁷>

P = {a, b², c², b²c², ad, bcd, ac³d, ad², c²d², ad³, be, ac²e, e², ae³, bf, bd²f, f², b²f², acdf², d²f², bf³, ad³f³, f⁴, ag, b²g, c²g, adg, bcdg, ac³dg, ad²g, c²d²g, cfg, cd²fg, f²g, ag², b²g², c²g², adg², bcdg², ad²g², c²d²g², cfg², cd²fg², f²g², ag³, adg³, ad²g³, h, ab²h, ac²h, abdh, acd²h, ad³fh, af²h, gh, ab²gh, ac²gh, acd²gh, g²h, acd²g²h, ah², b²h², d²h², agh², h³, i, ab²i, c³i, abcdi, d²i, abei, ac³ei, abfi, adfi, abd²fi, ad³fi, cf²i, bf³i, b³f³i, df³i, d³f³i, gi, ab²gi, abcdgi, d²gi, abfgi, adfgi, g²i, ab²g²i, abcdg²i, d²g²i, abfg²i, adfg²i, g³i, d²g³i, adfg³i, ahi, b²hi, bdhi, cd²hi, dfhi, d³fhi, aghi, b²ghi, cd²ghi, dfghi, ag²hi, dfg²hi, h²i, ab²h²i, ad²h²i, gh²i, ah³i, ai², b²i², c²i², bcdi², ad²i², c²d²i², bfi², dfi², bd²fi², d³fi², df³i², agi², c²gi², ad²gi², c²d²gi², ag²i², ad²g²i², hi², ab²hi², ac²hi², abdhi², acd²hi², ad³fhi², af²hi², ghi², g²hi², ah²i², d²h²i², i³, ab²i³, abcdi³, d²i³, abfi³, adfi³, abd²fi³, ad³fi³, gi³, d²gi³, adfgi³, ahi³, b²hi³, bdhi³, cd²hi³, dfhi³, d³fhi³, aghi³, h²i³, ad²h²i³, ai⁴, b²i⁴, c²i⁴, bcdi⁴, ad²i⁴, c²d²i⁴, bfi⁴, dfi⁴, bd²fi⁴, d³fi⁴, agi⁴, ad²gi⁴, hi⁴, ac²hi⁴, acd²hi⁴, ad³fhi⁴, af²hi⁴, ghi⁴, i⁵, ab²i⁵, abcdi⁵, d²i⁵, abfi⁵, adfi⁵, abd²fi⁵, ad³fi⁵, gi⁵, d²gi⁵, adfgi⁵, ahi⁵, cd²hi⁵, dfhi⁵, d³fhi⁵, aghi⁵, ai⁶, c²i⁶, ad²i⁶, c²d²i⁶, dfi⁶, d³fi⁶, agi⁶, ad²gi⁶, hi⁶, ac²hi⁶, acd²hi⁶, ad³fhi⁶, ghi⁶, aj, ab²cj, ac³j, ab²c³j, adj, c²dj, ad²j, ad³j, bej, abc²ej, ace²j, ab²fj, cdfj, df²j, agj, ab²cgj, adgj, c²dgj, ad²gj, abfgj, df²gj, ag²j, ab²cg²j, adg²j, c²dg²j, ad²g²j, abfg²j, df²g²j, ag³j, adg³j, ad²g³j, hj, bchj, b³chj, acd²hj, bfhj, ad²fhj, cghj, fghj, cg²hj, fg²hj, d²fg²hj, ah²j, abch²j, h³j, ij, ab²ij, ac²ij, ab²c²ij, abdij, acd²ij, abeij, bc²eij, af²ij, ad²f²ij, gij, ab²gij, ac²gij, abdgij, acd²gij, g²ij, ab²g²ij, abdg²ij, acd²g²ij, g³ij, ahij, b²hij, c²hij, bdhij, cd²hij, d³fhij, f²hij, b²ghij, c²ghij, cd²ghij, h²ij, ab²h²ij, ad²h²ij, ah³ij, ai²j, ab²ci²j, bdi²j, cd²i²j, ab²fi²j, dfi²j, d³fi²j, agi²j, bdgi²j, ag²i²j, hi²j, bchi²j, b³chi²j, acd²hi²j, ad²fhi²j, ah²i²j, i³j, ab²i³j, ac²i³j, abdi³j, acd²i³j, ad³fi³j, af²i³j, gi³j, acd²gi³j, ahi³j, b²hi³j, c²hi³j, bdhi³j, cd²hi³j, d³fhi³j, f²hi³j, h²i³j, ad²h²i³j, ai⁴j, ab²ci⁴j, bdi⁴j, cd²i⁴j, ab²fi⁴j, dfi⁴j, d²fi⁴j, d³fi⁴j, agi⁴j, hi⁴j, bchi⁴j, acd²hi⁴j, ad²fhi⁴j, i⁵j, ab²i⁵j, ac²i⁵j, abdi⁵j, acd²i⁵j, ad³fi⁵j, gi⁵j, acd²gi⁵j, ahi⁵j, c²hi⁵j, cd²hi⁵j, d³fhi⁵j, ai⁶j, cd²i⁶j, dfi⁶j, d²fi⁶j, d³fi⁶j, agi⁶j, hi⁶j, acd²hi⁶j, ad²fhi⁶j, aj², b²j², c²j², adj², bcdj², ac³dj², ad²j², c²d²j², ad³j², cfj², cd²fj², f²j², d²f²j², agj², b²gj², c²gj², adgj², ad²gj², ag²j², b²g²j², adg²j², ad²g²j², ag³j², adg³j², ad²g³j², ab²hj², ac²hj², abdhj², acd²hj², ad³fhj², af²hj², d²h²j², ij², b²cij², bcdij², d²ij², bfij², gij², bcgij², d²gij², cg²ij², b²cg²ij², fg²ij², d²fg²ij², d²g³ij², fg³ij², ahij², abchij², ab³chij², cd²hij², adfhij², ch²ij², ai²j², b²i²j², c²i²j², cd²i²j², d³fi²j², f²i²j², agi²j², ab²hi²j², ac²hi²j², acd²hi²j², ad³fhi²j², af²hi²j², ag²hi²j², ad²g²hi²j², i³j², bci³j², d²i³j², cgi³j², fgi³j², d²fgi³j², ahi³j², adfhi³j², ai⁴j², b²i⁴j², c²i⁴j², c²d²i⁴j², ac²hi⁴j², ac²d²hi⁴j², aghi⁴j², ad²ghi⁴j², i⁵j², bci⁵j², d²i⁵j², cgi⁵j², fgi⁵j², d²fgi⁵j², achi⁵j², afhi⁵j², ai⁶j², c²i⁶j², c²d²i⁶j², ac²hi⁶j², acd²hi⁶j², aghi⁶j², aj³, ab²cj³, ac³j³, adj³, c²dj³, ad²j³, ad³j³, abfj³, ab³fj³, cdfj³, df²j³, agj³, abcgj³, adgj³, c²dgj³, ad²gj³, hj³, bchj³, b³chj³, acd²hj³, cghj³, ij³, ab²ij³, ac²ij³, acd²ij³, af²ij³, ad²f²ij³, ag²ij³, c²hij³, cd²hij³, d³fhij³, ghij³, ai²j³, ad²i²j³, acgi²j³, acd²gi²j³, chi²j³, agi³j³, d²hi³j³, aci⁴j³, ad²i⁴j³, afi⁴j³, acgi⁴j³, acd²gi⁴j³, agi⁵j³, hi⁵j³, d²hi⁵j³, aci⁶j³, ad²i⁶j³, afi⁶j³, acgi⁶j³, ad²gi⁶j³, aj⁴, b²j⁴, c²j⁴, adj⁴, bcdj⁴, ad²j⁴, c²d²j⁴, ad³j⁴, cfj⁴, cd²fj⁴, f²j⁴, d²f²j⁴, b²gj⁴, c²gj⁴, adgj⁴, acd²hj⁴, ad³fhj⁴, ij⁴, b²cij⁴, d²ij⁴, bfij⁴, d²gij⁴, gi²j⁴, d²gi²j⁴, i⁴j⁴, gi⁴j⁴, d²gi⁴j⁴, i⁶j⁴, gi⁶j⁴, aj⁵, ab²cj⁵, adj⁵, c²dj⁵, ad²j⁵, abfj⁵, df²j⁵, agj⁵, adgj⁵, c²dgj⁵, ij⁵, ab²ij⁵, acd²ij⁵, aj⁶, b²j⁶, c²j⁶, adj⁶, ad²j⁶, adgj⁶, ij⁶, aj⁷, abcj⁷, adj⁷, c²dj⁷, b²j⁸, adj⁸}

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

Monoid Structure