Infinite cancellative non-commutative monoids, one auxiliary generator

Up:Monoids with two generators and one relation
174 unique, 175 total

Solved by magic:0

Σ#PresentationDescriptionRelated
6110⟨a, b | abab=ba⟩Infinite cancellative non-commutative monoid
6123⟨a, b | bab=aba⟩Infinite cancellative non-commutative monoid
8445⟨a, b | aabaab=ba⟩Infinite cancellative non-commutative monoid
8474⟨a, b | ababab=ba⟩Infinite cancellative non-commutative monoid
8541⟨a, b | abaab=baa⟩Infinite cancellative non-commutative monoid
8549⟨a, b | ababa=bab⟩Infinite cancellative non-commutative monoid
8586⟨a, b | baab=aaba⟩Infinite cancellative non-commutative monoid
8587⟨a, b | baab=abba⟩Infinite cancellative non-commutative monoid
8589⟨a, b | baba=abab⟩Infinite cancellative non-commutative monoid
9976⟨a, b | abaabab=ba⟩Infinite cancellative non-commutative monoid
91065⟨a, b | aabaab=baa⟩Infinite cancellative non-commutative monoid
91107⟨a, b | abaaab=baa⟩Infinite cancellative non-commutative monoid
91132⟨a, b | abbaab=baa⟩Infinite cancellative non-commutative monoid
91232⟨a, b | aabba=baab⟩Infinite cancellative non-commutative monoid
91272⟨a, b | abbba=baab⟩Infinite cancellative non-commutative monoid
91273⟨a, b | abbba=babb⟩Infinite cancellative non-commutative monoid
101883⟨a, b | aaabaaab=ba⟩Infinite cancellative non-commutative monoid
101960⟨a, b | aababaab=ba⟩Infinite cancellative non-commutative monoid
102028⟨a, b | abaaabab=ba⟩Infinite cancellative non-commutative monoid
102055⟨a, b | abababab=ba⟩Infinite cancellative non-commutative monoid
102211⟨a, b | aabaaab=baa⟩Infinite cancellative non-commutative monoid
102259⟨a, b | aabbaab=bba⟩Infinite cancellative non-commutative monoid
102303⟨a, b | abaaaba=bab⟩Infinite cancellative non-commutative monoid
102309⟨a, b | abaabab=baa⟩Infinite cancellative non-commutative monoid
102325⟨a, b | ababaab=baa⟩Infinite cancellative non-commutative monoid
102347⟨a, b | abbaaab=baa⟩Infinite cancellative non-commutative monoid
102349⟨a, b | abbaaab=bba⟩Infinite cancellative non-commutative monoid
102355⟨a, b | abbabba=bab⟩Infinite cancellative non-commutative monoid
102489⟨a, b | aabaab=baba⟩Infinite cancellative non-commutative monoid
102504⟨a, b | aababa=baab⟩Infinite cancellative non-commutative monoid
102571⟨a, b | abaaab=baaa⟩Infinite cancellative non-commutative monoid
102573⟨a, b | abaaab=baba⟩Infinite cancellative non-commutative monoid
102586⟨a, b | abaaba=baab⟩Infinite cancellative non-commutative monoid
102612⟨a, b | ababba=bbab⟩Infinite cancellative non-commutative monoid
102632⟨a, b | abbbba=baab⟩Infinite cancellative non-commutative monoid
102633⟨a, b | abbbba=babb⟩Infinite cancellative non-commutative monoid
102743⟨a, b | baaab=aabaa⟩Infinite cancellative non-commutative monoid
102744⟨a, b | baaab=aabba⟩Infinite cancellative non-commutative monoid
102745⟨a, b | baaab=ababa⟩Infinite cancellative non-commutative monoid
102746⟨a, b | baaab=abbba⟩Infinite cancellative non-commutative monoid
102752⟨a, b | baaba=abbab⟩Infinite cancellative non-commutative monoid
102759⟨a, b | baabb=abbaa⟩Infinite cancellative non-commutative monoid
102767⟨a, b | babab=ababa⟩Infinite cancellative non-commutative monoid
114086⟨a, b | aabaabaab=ba⟩Infinite cancellative non-commutative monoid
114234⟨a, b | abaaaabab=ba⟩Infinite cancellative non-commutative monoid
114265⟨a, b | abaababab=ba⟩Infinite cancellative non-commutative monoid
114487⟨a, b | aaabaaab=baa⟩Infinite cancellative non-commutative monoid
114685⟨a, b | aabbaaab=bba⟩Infinite cancellative non-commutative monoid
114698⟨a, b | aabbaabb=baa⟩Infinite cancellative non-commutative monoid
114721⟨a, b | aabbbaab=bba⟩Infinite cancellative non-commutative monoid
114765⟨a, b | abaaaaba=bab⟩Infinite cancellative non-commutative monoid
114771⟨a, b | abaaabab=baa⟩Infinite cancellative non-commutative monoid
114787⟨a, b | abaabaab=baa⟩Infinite cancellative non-commutative monoid
114796⟨a, b | abaababa=bab⟩Infinite cancellative non-commutative monoid
114802⟨a, b | abaabbab=baa⟩Infinite cancellative non-commutative monoid
114837⟨a, b | ababbaab=bba⟩Infinite cancellative non-commutative monoid
114859⟨a, b | abbaaaab=bba⟩Infinite cancellative non-commutative monoid
114882⟨a, b | abbbaaab=baa⟩Infinite cancellative non-commutative monoid
115125⟨a, b | aabaaab=baaa⟩Infinite cancellative non-commutative monoid
115142⟨a, b | aabaaba=baab⟩Infinite cancellative non-commutative monoid
115172⟨a, b | aababaa=baab⟩Infinite cancellative non-commutative monoid
115219⟨a, b | aabbaab=bbaa⟩Infinite cancellative non-commutative monoid
115289⟨a, b | abaaaab=baaa⟩Infinite cancellative non-commutative monoid
115291⟨a, b | abaaaab=baba⟩Infinite cancellative non-commutative monoid
115332⟨a, b | abaabba=baab⟩Infinite cancellative non-commutative monoid
115336⟨a, b | abaabba=bbab⟩Infinite cancellative non-commutative monoid
115363⟨a, b | abababa=babb⟩Infinite cancellative non-commutative monoid
115389⟨a, b | abbaaab=baaa⟩Infinite cancellative non-commutative monoid
115393⟨a, b | abbaaab=bbaa⟩Infinite cancellative non-commutative monoid
115414⟨a, b | abbbbba=baab⟩Infinite cancellative non-commutative monoid
115614⟨a, b | aaabba=baaab⟩Infinite cancellative non-commutative monoid
115663⟨a, b | aabaab=baaba⟩Infinite cancellative non-commutative monoid
115739⟨a, b | aabbaa=baaab⟩Infinite cancellative non-commutative monoid
115794⟨a, b | aabbba=baaab⟩Infinite cancellative non-commutative monoid
115796⟨a, b | aabbba=baabb⟩Infinite cancellative non-commutative monoid
115802⟨a, b | aabbba=bbaab⟩Infinite cancellative non-commutative monoid
115894⟨a, b | ababba=baaab⟩Infinite cancellative non-commutative monoid
115902⟨a, b | ababba=bbaab⟩Infinite cancellative non-commutative monoid
115940⟨a, b | abbbba=baabb⟩Infinite cancellative non-commutative monoid
115941⟨a, b | abbbba=babab⟩Infinite cancellative non-commutative monoid
115942⟨a, b | abbbba=babbb⟩Infinite cancellative non-commutative monoid

Solved by morph:2/0

Σ#PresentationDescriptionRelated
91120⟨a, b | ababab=baa⟩Infinite cancellative non-commutative monoid
101712⟨a, b | aabbaaaba=b⟩Infinite cancellative non-commutative monoid
102311⟨a, b | abaabab=bba⟩Infinite cancellative non-commutative monoid
102318⟨a, b | abaabba=bab⟩Infinite cancellative non-commutative monoid
102327⟨a, b | ababaab=bba⟩Infinite cancellative non-commutative monoid
102597⟨a, b | ababab=baba⟩Infinite cancellative non-commutative monoid
102598⟨a, b | ababab=bbaa⟩Infinite cancellative non-commutative monoid
113536⟨a, b | aabaaaaaba=b⟩Infinite cancellative non-commutative monoid
113626⟨a, b | aabbaaaaba=b⟩Infinite cancellative non-commutative monoid
113646⟨a, b | aabbabaaba=b⟩Infinite cancellative non-commutative monoid
113665⟨a, b | aabbbaaaba=b⟩Infinite cancellative non-commutative monoid
114641⟨a, b | aababaab=bba⟩Infinite cancellative non-commutative monoid
114773⟨a, b | abaaabab=bba⟩Infinite cancellative non-commutative monoid
114780⟨a, b | abaaabba=bab⟩Infinite cancellative non-commutative monoid
114789⟨a, b | abaabaab=bba⟩Infinite cancellative non-commutative monoid
114817⟨a, b | ababaaab=bba⟩Infinite cancellative non-commutative monoid
114822⟨a, b | abababab=baa⟩Infinite cancellative non-commutative monoid
114835⟨a, b | ababbaab=baa⟩Infinite cancellative non-commutative monoid
114857⟨a, b | abbaaaab=baa⟩Infinite cancellative non-commutative monoid
114870⟨a, b | abbabaab=baa⟩Infinite cancellative non-commutative monoid
115232⟨a, b | aabbaba=baab⟩Infinite cancellative non-commutative monoid
115274⟨a, b | aabbbba=baab⟩Infinite cancellative non-commutative monoid
115317⟨a, b | abaabab=baba⟩Infinite cancellative non-commutative monoid
115319⟨a, b | abaabab=bbaa⟩Infinite cancellative non-commutative monoid
115351⟨a, b | ababaab=bbaa⟩Infinite cancellative non-commutative monoid
115939⟨a, b | abbbba=baaab⟩Infinite cancellative non-commutative monoid

Solved by morph:3/0

Σ#PresentationDescriptionRelated
7225⟨a, b | abaab=ba⟩Infinite cancellative non-commutative monoid
9860⟨a, b | abbaabba=b⟩Infinite cancellative non-commutative monoid1 iso
102036⟨a, b | abaabaab=ba⟩Infinite cancellative non-commutative monoid
102044⟨a, b | abaabbab=ba⟩Infinite cancellative non-commutative monoid
102077⟨a, b | abbaabba=bb⟩Infinite cancellative non-commutative monoid
102487⟨a, b | aabaab=baaa⟩Infinite cancellative non-commutative monoid
114242⟨a, b | abaaabaab=ba⟩Infinite cancellative non-commutative monoid
114250⟨a, b | abaaabbab=ba⟩Infinite cancellative non-commutative monoid
114273⟨a, b | abaabbaab=ba⟩Infinite cancellative non-commutative monoid
115217⟨a, b | aabbaab=baba⟩Infinite cancellative non-commutative monoid
115315⟨a, b | abaabab=baaa⟩Infinite cancellative non-commutative monoid
115404⟨a, b | abbabba=baab⟩Infinite cancellative non-commutative monoid
115405⟨a, b | abbabba=babb⟩Infinite cancellative non-commutative monoid
115667⟨a, b | aabaab=babba⟩Infinite cancellative non-commutative monoid
115694⟨a, b | aababa=baaab⟩Infinite cancellative non-commutative monoid
115740⟨a, b | aabbaa=baabb⟩Infinite cancellative non-commutative monoid
115857⟨a, b | abaaba=babab⟩Infinite cancellative non-commutative monoid

Solved by morph:4/0

Σ#PresentationDescriptionRelated
8467⟨a, b | abaaab=ba⟩Infinite cancellative non-commutative monoid
9950⟨a, b | aabbaab=ba⟩Infinite cancellative non-commutative monoid
101810⟨a, b | abbababba=b⟩Infinite cancellative non-commutative monoid
113826⟨a, b | abbbaabbba=b⟩Infinite cancellative non-commutative monoid
114639⟨a, b | aababaab=baa⟩Infinite cancellative non-commutative monoid
114815⟨a, b | ababaaab=baa⟩Infinite cancellative non-commutative monoid
115831⟨a, b | abaaab=babba⟩Infinite cancellative non-commutative monoid

Solved by morph:5/0

Σ#PresentationDescriptionRelated
9984⟨a, b | ababaab=ba⟩Infinite cancellative non-commutative monoid
101937⟨a, b | aabaaaab=ba⟩Infinite cancellative non-commutative monoid
102002⟨a, b | aabbbaab=ba⟩Infinite cancellative non-commutative monoid
102340⟨a, b | ababbba=bab⟩Infinite cancellative non-commutative monoid
113808⟨a, b | abbaababba=b⟩Infinite cancellative non-commutative monoid
114012⟨a, b | aaabbaaab=ba⟩Infinite cancellative non-commutative monoid
114110⟨a, b | aababaaab=ba⟩Infinite cancellative non-commutative monoid
114331⟨a, b | abbaaabba=bb⟩Infinite cancellative non-commutative monoid
114808⟨a, b | abaabbba=bab⟩Infinite cancellative non-commutative monoid
114843⟨a, b | ababbaba=bab⟩Infinite cancellative non-commutative monoid
115215⟨a, b | aabbaab=baaa⟩Infinite cancellative non-commutative monoid
115378⟨a, b | ababbba=bbab⟩Infinite cancellative non-commutative monoid

Solved by morph:6/0

Σ#PresentationDescriptionRelated
114063⟨a, b | aabaaaaab=ba⟩Infinite cancellative non-commutative monoid
114308⟨a, b | ababbaaab=ba⟩Infinite cancellative non-commutative monoid
114316⟨a, b | ababbbaab=ba⟩Infinite cancellative non-commutative monoid
114850⟨a, b | ababbbba=bab⟩Infinite cancellative non-commutative monoid
115127⟨a, b | aabaaab=baba⟩Infinite cancellative non-commutative monoid
115391⟨a, b | abbaaab=baba⟩Infinite cancellative non-commutative monoid
115922⟨a, b | abbaab=baaba⟩Infinite cancellative non-commutative monoid

Solved by morph:7/0

Σ#PresentationDescriptionRelated
113744⟨a, b | abaabbaaba=b⟩Infinite cancellative non-commutative monoid

Solved by morph:2/1

Σ#PresentationDescriptionRelated
115347⟨a, b | ababaab=baaa⟩Infinite cancellative non-commutative monoid

Solved by morph:3/1

Σ#PresentationDescriptionRelated
9927⟨a, b | aabaaab=ba⟩Infinite cancellative non-commutative monoid
91126⟨a, b | ababba=bab⟩Infinite cancellative non-commutative monoid
102750⟨a, b | baaba=abaab⟩Infinite cancellative non-commutative monoid
102756⟨a, b | baabb=aabba⟩Infinite cancellative non-commutative monoid
113957⟨a, b | aaabaaaab=ba⟩Infinite cancellative non-commutative monoid

Solved by morph:4/1

Σ#PresentationDescriptionRelated
102295⟨a, b | abaaaab=baa⟩Infinite cancellative non-commutative monoid
102556⟨a, b | aabbba=baab⟩Infinite cancellative non-commutative monoid

Solved by morph:5/1

Σ#PresentationDescriptionRelated
9969⟨a, b | abaaaab=ba⟩Infinite cancellative non-commutative monoid
102062⟨a, b | ababbaab=ba⟩Infinite cancellative non-commutative monoid
114593⟨a, b | aabaaaab=baa⟩Infinite cancellative non-commutative monoid
115415⟨a, b | abbbbba=babb⟩Infinite cancellative non-commutative monoid
115898⟨a, b | ababba=babab⟩Infinite cancellative non-commutative monoid

Solved by morph:6/1

Σ#PresentationDescriptionRelated
102021⟨a, b | abaaaaab=ba⟩Infinite cancellative non-commutative monoid
114757⟨a, b | abaaaaab=baa⟩Infinite cancellative non-commutative monoid
114828⟨a, b | abababba=bab⟩Infinite cancellative non-commutative monoid

Solved by morph:3/2

Σ#PresentationDescriptionRelated
102608⟨a, b | ababba=baab⟩Infinite cancellative non-commutative monoid

Solved by morph:4/2

Σ#PresentationDescriptionRelated
115200⟨a, b | aababba=baab⟩Infinite cancellative non-commutative monoid

Solved by morph:6/2

Σ#PresentationDescriptionRelated
114133⟨a, b | aababbaab=ba⟩Infinite cancellative non-commutative monoid

Solved by morph:7/2

Σ#PresentationDescriptionRelated
114227⟨a, b | abaaaaaab=ba⟩Infinite cancellative non-commutative monoid

Solved by morph:7/3

Σ#PresentationDescriptionRelated
114258⟨a, b | abaabaaab=ba⟩Infinite cancellative non-commutative monoid

Solved by morph:7/5

Σ#PresentationDescriptionRelated
114297⟨a, b | abababaab=ba⟩Infinite cancellative non-commutative monoid

Solved by morph:4/6

Σ#PresentationDescriptionRelated
115304⟨a, b | abaaaba=baab⟩Infinite cancellative non-commutative monoid