Details Page for 0.3036

Complete Solution is Known:

MSV File: q-0.3036.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₂₇(0.3036):

Q = <a,b,c,d,e,f,g,h,i,j,k | a²=1, b⁴=b², b²c=ab³, c²=1, bd²=b, d³=d, b³e=be, bce=ab²e, d²e³=e³, b²e⁴=e⁴, ce⁴=abe⁴, e⁵=ae⁴, b³f=bf, bcf=ab²f, d²f=f, b²ef=ef, cef=abef, b²f²=f², cf²=abf², e⁴f³=ae³f³, e³f⁴=ae⁴f², f⁶=f⁴, bg=bc, e³g=abe³, fg=cf, de²g²=b²de², g³=cg², de²gh=abde²h, g²h=cgh, b²de²h²=de²h², cde²h²=abde²h², d²e²h²=b²e²h², e³h²=b²e³, gh²=ch², h³=cgh, bi=bd, d²i=i, e⁴i=de⁴, fi=df, g²i=dg², ghi=dgh, h²i=dh², i²=d²g², b³j=bj, bcj=ab²j, e⁴j=ade⁴, b²fj=fj, cfj=abfj, e³f³j=ade³f³, deg²j=b²dej, deghj=abdehj, b²deh²j=deh²j, cdeh²j=abdeh²j, d²eh²j=b²eh²j, e²j²=b²e², f³j²=f³, dg²j²=b²dj², dghj²=abdhj², b²dh²j²=dh²j², cdh²j²=abdh²j², d²h²j²=b²h²j², ej³=b²ej, j⁴=b²j², b³k=bk, bck=ab²k, d²e²k=e²k, e⁴k=e⁴, b²fk=fk, cfk=abfk, e³f²k=ae⁴f², degk=abdek, e²gk=abe²k, g²k=cgk, b²deh²k=deh²k, cdeh²k=abdeh²k, d²eh²k=b²eh²k, b²e²h²k=e²h²k, ce²h²k=abe²h²k, gik=dgk, dgjk=abdjk, b²dh²jk=dh²jk, cdh²jk=abdh²jk, d²h²jk=b²h²jk, b²dj²k=dj²k, cdj²k=abdj²k, d²j²k=b²j²k, b²ej²k=ej²k, cej²k=abej²k, gj²k=cj²k, ij²k=dj²k, b²j³k=j³k, cj³k=abj³k, d²ek²=ek², e³k²=e³k, f³k²=f⁵, dgk²=abdk², egk²=abek², b²dh²k²=dh²k², cdh²k²=abdh²k², d²h²k²=b²h²k², b²eh²k²=eh²k², ceh²k²=abeh²k², b²j²k²=j²k², cj²k²=abj²k², j³k²=b²jk², d²k³=k³, gk³=abk³, b²h²k³=h²k³, ch²k³=abh²k³, j²k³=b²k³, e²k⁴=e²k², k⁵=k³>

P = {a, b², c, ad, cd, ad², cd², be, e², b²e², d²e², ae³, ab²e³, e⁴, abf, aef, abe²f, be³f, abe⁴f, f², bef², e²f², ae³f², e⁴f², af³, abef³, bde²f³, abde³f³, f⁴, bef⁴, e²f⁴, af⁵, abef⁵, bde²f⁵, g, acg, dg, acdg, d²g, acd²g, ce²g, cd²e²g, ag², cg², adg², cdg², ad²g², cd²g², e²g², ah, ch, adh, b²dh, cdh, ad²h, cd²h, bdeh, ace²h, de²h, b²de²h, abe³h, ce³h, be⁴h, abdfh, adefh, abde²fh, e³fh, ae⁴fh, df²h, bdef²h, de²f²h, abe³f²h, be⁴f²h, adf³h, abdef³h, be²f³h, e³f³h, df⁴h, bdef⁴h, de²f⁴h, adf⁵h, abdef⁵h, be²f⁵h, gh, acgh, dgh, acdgh, d²gh, acd²gh, ae²gh, ah², b²h², ch², adh², cdh², ad²h², cd²h², beh², e²h², b²e²h², abfh², aefh², abe²fh², f²h², bef²h², e²f²h², af³h², abef³h², bde²f³h², f⁴h², bef⁴h², e²f⁴h², af⁵h², abef⁵h², bde²f⁵h², ai, ci, adi, cdi, de²i, ade³i, gi, acgi, dgi, acdgi, cde²gi, ahi, chi, adhi, cdhi, e²hi, cde³hi, bj, ej, b²ej, d²ej, be²j, ade²j, de³j, b²de³j, afj, abefj, ae²fj, abde³fj, bf²j, ef²j, be²f²j, de³f²j, abf³j, aef³j, abe²f³j, bf⁴j, ef⁴j, ade²f⁴j, abf⁵j, aef⁵j, abe²f⁵j, cegj, cd²egj, eg²j, bdhj, acehj, dehj, b²dehj, bde²hj, acde³hj, adfhj, abdefhj, ade²fhj, bdf²hj, def²hj, bde²f²hj, abdf³hj, adef³hj, abde²f³hj, bdf⁴hj, def⁴hj, ae²f⁴hj, abdf⁵hj, adef⁵hj, abde²f⁵hj, aeghj, bh²j, eh²j, b²eh²j, be²h²j, afh²j, abefh²j, ae²fh²j, bf²h²j, ef²h²j, be²f²h²j, abf³h²j, aef³h²j, abe²f³h²j, bf⁴h²j, ef⁴h²j, ade²f⁴h²j, abf⁵h²j, aef⁵h²j, abe²f⁵h²j, deij, ae²ij, e³ij, cdegij, ehij, ace³hij, j², b²j², d²j², bej², adej², abfj², aefj², f²j², bef²j², cgj², cd²gj², g²j², achj², dhj², b²dhj², bdehj², abdfhj², adefhj², df²hj², bdef²hj², aghj², h²j², b²h²j², beh²j², abfh²j², aefh²j², f²h²j², bef²h²j², dij², aeij², cdgij², hij², bj³, adj³, afj³, bf²j³, bdhj³, adfhj³, bdf²hj³, bh²j³, afh²j³, bf²h²j³, aij³, abk, aek, ab²ek, ad²ek, e²k, b²e²k, ae³k, ab²e³k, fk, befk, abe²fk, be³fk, af²k, e²f²k, f³k, bef³k, af⁴k, abef⁴k, f⁵k, bef⁵k, ade²f⁵k, acegk, abdhk, cehk, adehk, ab²dehk, de²hk, b²de²hk, abe³hk, ce³hk, dfhk, bdefhk, abde²fhk, e³fhk, abf²hk, aef²hk, de²f²hk, df³hk, bdef³hk, adf⁴hk, abdef⁴hk, df⁵hk, bdef⁵hk, ae²f⁵hk, eghk, abh²k, aeh²k, ab²eh²k, e²h²k, fh²k, befh²k, abe²fh²k, abdf²h²k, adef²h²k, e²f²h²k, f³h²k, bef³h²k, af⁴h²k, abef⁴h²k, f⁵h²k, bef⁵h²k, ade²f⁵h²k, adeik, de²ik, ade³ik, aehik, e²hik, cde³hik, ajk, ab²jk, ad²jk, abejk, cd²ejk, be²jk, ace²jk, de³jk, b²de³jk, bfjk, efjk, ae²fjk, abde³fjk, abef²jk, bf³jk, ef³jk, abf⁴jk, aef⁴jk, bde²f⁴jk, bf⁵jk, ef⁵jk, acgjk, chjk, adhjk, ab²dhjk, abdehjk, cdehjk, bde²hjk, acde³hjk, bdfhjk, defhjk, ade²fhjk, af²hjk, abdef²hjk, bdf³hjk, def³hjk, abdf⁴hjk, adef⁴hjk, e²f⁴hjk, bdf⁵hjk, def⁵hjk, ghjk, ah²jk, ab²h²jk, abeh²jk, be²h²jk, bfh²jk, efh²jk, ae²fh²jk, adf²h²jk, abef²h²jk, bf³h²jk, ef³h²jk, abf⁴h²jk, aef⁴h²jk, bf⁵h²jk, ef⁵h²jk, adijk, cdeijk, acde²ijk, e³ijk, ahijk, cehijk, ace³hijk, abj²k, aej²k, fj²k, befj²k, abf²j²k, aef²j²k, abdhj²k, adehj²k, dfhj²k, bdefhj²k, abdf²hj²k, adef²hj²k, abh²j²k, aeh²j²k, fh²j²k, befh²j²k, abf²h²j²k, aef²h²j²k, aj³k, bfj³k, af²j³k, adhj³k, bdfhj³k, adf²hj³k, ah²j³k, bfh²j³k, af²h²j³k, k², b²k², d²k², aek², ab²ek², e²k², b²e²k², abfk², befk², abe²fk², f²k², adef²k², e²f²k², cgk², achk², dhk², b²dhk², adehk², ab²dehk², de²hk², b²de²hk², abdfhk², bdefhk², abde²fhk², df²hk², aef²hk², de²f²hk², aghk², h²k², b²h²k², aeh²k², e²h²k², abfh²k², befh²k², abe²fh²k², f²h²k², adef²h²k², e²f²h²k², dik², adeik², de²ik², hik², aehik², e²hik², bjk², acd²jk², abejk², cejk², be²jk², ace²jk², afjk², efjk², ae²fjk², bf²jk², be²f²jk², bdhjk², acdhjk², abdehjk², cdehjk², bde²hjk², adfhjk², defhjk², ade²fhjk², bdf²hjk², bh²jk², abeh²jk², be²h²jk², afh²jk², efh²jk², ae²fh²jk², bf²h²jk², be²f²h²jk², acdijk², cdeijk², acde²ijk², achijk², cehijk², j²k², aej²k², abfj²k², befj²k², f²j²k², dhj²k², adehj²k², abdfhj²k², bdefhj²k², df²hj²k², h²j²k², aeh²j²k², abfh²j²k², befh²j²k², f²h²j²k², k³, b²k³, aek³, ab²ek³, e²k³, b²e²k³, abfk³, befk³, abe²fk³, def²k³, dhk³, b²dhk³, adehk³, ab²dehk³, de²hk³, b²de²hk³, abdfhk³, bdefhk³, abde²fhk³, ef²hk³, h²k³, aeh²k³, e²h²k³, abfh²k³, befh²k³, abe²fh²k³, def²h²k³, dik³, adeik³, de²ik³, hik³, aehik³, e²hik³, bjk³, acjk³, abejk³, cejk³, be²jk³, ace²jk³, afjk³, efjk³, ae²fjk³, bdef²jk³, bdhjk³, acdhjk³, abdehjk³, cdehjk³, bde²hjk³, adfhjk³, defhjk³, ade²fhjk³, bef²hjk³, abe²f²hjk³, bh²jk³, abeh²jk³, be²h²jk³, afh²jk³, efh²jk³, ae²fh²jk³, bdef²h²jk³, acdijk³, cdeijk³, acde²ijk³, achijk³, cehijk³, k⁴, b²k⁴, aek⁴, ab²ek⁴, abfk⁴, befk⁴, f²k⁴, adef²k⁴, dhk⁴, b²dhk⁴, adehk⁴, ab²dehk⁴, abdfhk⁴, bdefhk⁴, df²hk⁴, aef²hk⁴, h²k⁴, aeh²k⁴, abfh²k⁴, befh²k⁴, f²h²k⁴, adef²h²k⁴, dik⁴, adeik⁴, hik⁴, aehik⁴, bjk⁴, acjk⁴, abejk⁴, cejk⁴, afjk⁴, efjk⁴, bf²jk⁴, abdef²jk⁴, bdhjk⁴, acdhjk⁴, abdehjk⁴, cdehjk⁴, adfhjk⁴, defhjk⁴, bdf²hjk⁴, bh²jk⁴, abeh²jk⁴, afh²jk⁴, efh²jk⁴, bf²h²jk⁴, abdef²h²jk⁴, acdijk⁴, cdeijk⁴, achijk⁴, cehijk⁴}

Phi = 1 a 1 a 1 b ab b a 1 a 1 b ab b c cdg adg² d e f b g h adg² i j k

Monoid Structure