Infinite cancellative non-commutative monoids

Up:Monoid enumeration
124 unique, 333 total

Σ#PresentationPropertiesDescriptionφ
57⟨a, b, c | aa=b, cc=1⟩Can Infℤ2 ∗ ℕ65
642⟨a, b, c | ba=ab, cc=1⟩Can Infℤ2 ∗ (ℕ ⊕ ℕ)
653⟨a, b, c | bc=ac, cc=1⟩Can Infℤ2 ∗ ℕ8
699⟨a, b, c | aa=b, ccc=1⟩Can Infℤ3 ∗ ℕ25
6146⟨a, b, c | aa=b, cc=b⟩Can Inf5
6160⟨a, b, c | ab=c, bc=a⟩Can Inf3
7445⟨a, b, c | ac=ab, aaa=1⟩Can Infℤ3 ∗ ℕ1
7465⟨a, b, c | ba=ab, ccc=1⟩Can Infℤ3 ∗ (ℕ ⊕ ℕ)
7533⟨a, b, c | ba=ab, cc=a⟩Can Inf
7537⟨a, b, c | ba=ac, bb=c⟩Can Inf4
7543⟨a, b, c | ba=ac, cb=a⟩Can Inf
7548⟨a, b, c | bb=aa, cc=a⟩Can Inf1
7554⟨a, b, c | bb=ac, ca=b⟩Can Inf3
7555⟨a, b, c | bb=ac, cb=a⟩Can Inf4
7558⟨a, b, c | bb=ac, cc=a⟩Can Inf2
7774⟨a, b, c | aa=b, cccc=1⟩Can Infℤ4 ∗ ℕ8
7913⟨a, b, c | aa=b, aca=c⟩Can Inf4
7916⟨a, b, c | aa=b, acb=c⟩Can Inf2
7930⟨a, b, c | aa=b, bcb=c⟩Can Inf4
7937⟨a, b, c | aa=b, cbc=a⟩Can Inf2
7938⟨a, b, c | aa=b, cbc=b⟩Can Inf5
71024⟨a, b, c | ab=c, aca=b⟩Can Inf3
71041⟨a, b, c | ab=c, bca=c⟩Can Inf2
71042⟨a, b, c | ab=c, bcc=a⟩Can Inf2
82830⟨a, b, c | aaa=b, acb=c⟩Can Inf1
82844⟨a, b, c | aaa=b, bcb=c⟩Can Inf
82849⟨a, b, c | aaa=b, cac=b⟩Can Inf2
82851⟨a, b, c | aaa=b, cbc=a⟩Can Inf3
82852⟨a, b, c | aaa=b, cbc=b⟩Can Inf
82854⟨a, b, c | aaa=b, ccc=b⟩Can Inf1
82970⟨a, b, c | aab=c, aca=b⟩Can Inf3
82976⟨a, b, c | aab=c, baa=c⟩Can Inf2
82983⟨a, b, c | aab=c, bba=c⟩Can Inf
82984⟨a, b, c | aab=c, bbc=a⟩Can Inf5
82987⟨a, b, c | aab=c, bca=c⟩Can Inf
82988⟨a, b, c | aab=c, bcb=a⟩Can Inf2
82991⟨a, b, c | aab=c, bcc=a⟩Can Inf
83031⟨a, b, c | aba=b, aca=c⟩Can Inf
83034⟨a, b, c | aba=b, acb=c⟩Can Inf
83040⟨a, b, c | aba=b, bcb=c⟩Can Inf
83041⟨a, b, c | aba=b, cac=b⟩Can Inf
83042⟨a, b, c | aba=b, cbc=a⟩Can Inf1
83043⟨a, b, c | aba=b, cbc=b⟩Can Inf
83045⟨a, b, c | aba=c, abc=b⟩Can Inf2
83051⟨a, b, c | aba=c, bab=c⟩Can Inf
83071⟨a, b, c | abc=b, bca=c⟩Can Inf2
83072⟨a, b, c | abc=b, cba=b⟩Can Inf
83138⟨a, b, c | ac=ab, aaaa=1⟩Can Infℤ4 ∗ ℕ
83197⟨a, b, c | ba=ab, cccc=1⟩Can Infℤ4 ∗ (ℕ ⊕ ℕ)
83424⟨a, b, c | ba=ab, aca=c⟩Can Inf
83426⟨a, b, c | ba=ab, acb=c⟩Can Inf
83430⟨a, b, c | ba=ab, cac=a⟩Can Inf
83431⟨a, b, c | ba=ab, cac=b⟩Can Inf
83433⟨a, b, c | ba=ab, ccc=a⟩Can Inf
83439⟨a, b, c | ba=ac, aab=c⟩Can Inf3
83448⟨a, b, c | ba=ac, abb=c⟩Can Inf3
83465⟨a, b, c | ba=ac, bbb=c⟩Can Inf1
83471⟨a, b, c | ba=ac, bcb=c⟩Can Inf
83472⟨a, b, c | ba=ac, cab=a⟩Can Inf
83474⟨a, b, c | ba=ac, cbb=a⟩Can Inf
83488⟨a, b, c | bb=aa, aca=c⟩Can Inf
83490⟨a, b, c | bb=aa, acb=c⟩Can Inf
83494⟨a, b, c | bb=aa, cac=a⟩Can Inf
83495⟨a, b, c | bb=aa, cac=b⟩Can Inf
83497⟨a, b, c | bb=aa, ccc=a⟩Can Inf
83501⟨a, b, c | bb=ac, aaa=c⟩Can Inf2
83510⟨a, b, c | bb=ac, aba=c⟩Can Inf2
83524⟨a, b, c | bb=ac, baa=c⟩Can Inf2
83535⟨a, b, c | bb=ac, bca=c⟩Can Inf
83537⟨a, b, c | bb=ac, caa=b⟩Can Inf
83540⟨a, b, c | bb=ac, cba=b⟩Can Inf
83584⟨a, b, c | ba=ab, ca=ac⟩Can Inf
83585⟨a, b, c | ba=ab, ca=bc⟩Can Inf
83586⟨a, b, c | ba=ab, cc=aa⟩Can Inf
83587⟨a, b, c | ba=ab, cc=ab⟩Can Inf1
83592⟨a, b, c | ba=ac, ca=ab⟩Can Inf
83593⟨a, b, c | ba=ac, ca=bb⟩Can Inf
83594⟨a, b, c | ba=ac, cb=aa⟩Can Inf
83595⟨a, b, c | ba=ac, cb=ac⟩Can Inf
83596⟨a, b, c | ba=ac, cc=bb⟩Can Inf
83598⟨a, b, c | bb=aa, cc=aa⟩Can Inf
83599⟨a, b, c | bb=aa, cc=ab⟩Can Inf
83602⟨a, b, c | bb=ac, cb=aa⟩Can Inf
84375⟨a, b, c | aba=1, aabc=c⟩Can Infℕ ∗ ℤ2
84771⟨a, b, c | aa=b, ccccc=1⟩Can Infℤ5 ∗ ℕ1
85192⟨a, b, c | aa=b, abcb=c⟩Can Inf1
85204⟨a, b, c | aa=b, acbb=c⟩Can Inf
85240⟨a, b, c | aa=b, bbcb=c⟩Can Inf
85252⟨a, b, c | aa=b, bccb=c⟩Can Inf
85260⟨a, b, c | aa=b, cabc=b⟩Can Inf
85265⟨a, b, c | aa=b, cbbc=a⟩Can Inf
85266⟨a, b, c | aa=b, cbbc=b⟩Can Inf
85269⟨a, b, c | aa=b, cbcc=b⟩Can Inf
85567⟨a, b, c | ab=c, baca=c⟩Can Inf
85568⟨a, b, c | ab=c, bacc=a⟩Can Inf
85581⟨a, b, c | ab=c, bbca=c⟩Can Inf1
85585⟨a, b, c | ab=c, bcac=a⟩Can Inf
85592⟨a, b, c | ab=c, bcca=c⟩Can Inf
85663⟨a, b, c | aa=b, aaa=cc⟩Can Inf1
85674⟨a, b, c | aa=b, aac=bc⟩Can Infℕ ∗ ℕ3
85675⟨a, b, c | aa=b, aac=ca⟩Can Inf1
85685⟨a, b, c | aa=b, abb=cc⟩Can Inf1
85693⟨a, b, c | aa=b, abc=cb⟩Can Inf1
85717⟨a, b, c | aa=b, acc=cb⟩Can Inf1
85733⟨a, b, c | aa=b, bbb=cc⟩Can Inf
85740⟨a, b, c | aa=b, bbc=ca⟩Can Inf
85741⟨a, b, c | aa=b, bbc=cb⟩Can Inf
85748⟨a, b, c | aa=b, bcb=cc⟩Can Inf
85756⟨a, b, c | aa=b, bcc=cb⟩Can Inf
85761⟨a, b, c | aa=b, cac=bb⟩Can Inf
85765⟨a, b, c | aa=b, cbc=ab⟩Can Inf
85767⟨a, b, c | aa=b, cbc=bb⟩Can Inf
85773⟨a, b, c | aa=b, ccc=bb⟩Can Inf
86019⟨a, b, c | ab=c, aba=bc⟩Can Inf
86037⟨a, b, c | ab=c, aca=bc⟩Can Inf1
86064⟨a, b, c | ab=c, baa=cc⟩Can Inf1
86071⟨a, b, c | ab=c, bac=ca⟩Can Inf
86088⟨a, b, c | ab=c, bca=cc⟩Can Inf
86089⟨a, b, c | ab=c, bcc=aa⟩Can Inf
86095⟨a, b, c | ab=c, bcc=ca⟩Can Inf
86101⟨a, b, c | ab=c, cac=ba⟩Can Inf
86110⟨a, b, c | ab=c, ccc=ba⟩Can Inf
87138⟨a, b, c | aa=1, aabc=bc⟩Can Infℤ2 ∗ ℕ ∗ ℕ1
87140⟨a, b, c | aa=1, aabc=cb⟩Can Infℤ2 ∗ (ℕ ⊕ ℕ)2