Infinite non-Abelian groups, one auxiliary generator

Up:Monoids with two generators and two relations
10 unique, 65 total

Solved by frequency:2/0

Σ#PresentationDescriptionRelated
8485⟨a, b | aabb=1, abba=1⟩Infinite non-Abelian group14 iso
81046⟨a, b | aa=1, abbabb=1⟩Infinite non-Abelian group22 iso, 2 anti-iso
104275⟨a, b | aaabb=1, aabba=1⟩Infinite non-Abelian group8 iso
105730⟨a, b | aaaa=1, bbabb=a⟩Infinite non-Abelian group
105903⟨a, b | abab=1, aabaa=b⟩Infinite non-Abelian group
107546⟨a, b | aaa=1, bbaabb=a⟩Infinite non-Abelian group3 iso
1126090⟨a, b | aa=1, abbabbabb=1⟩Infinite non-Abelian group2 iso

Solved by frequency:2/1

Σ#PresentationDescriptionRelated
107542⟨a, b | aaa=1, babbab=a⟩Infinite non-Abelian group1 iso

Solved by frequency:3/0

Σ#PresentationDescriptionRelated
104084⟨a, b | baa=aab, abab=1⟩Infinite non-Abelian group1 iso

Solved by frequency:3/1

Σ#PresentationDescriptionRelated
109478⟨a, b | aa=1, abbbabbb=1⟩Infinite non-Abelian group2 iso