Infinite non-Abelian groups, one auxiliary generator

Up:Monoids with two generators and one relation

17 unique, 26 total

Solved by frequency:2/1

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101392⟨a, b | aabaaaaaba=1⟩Infinite non-Abelian group

Solved by frequency:3/0

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9665⟨a, b | aababaaab=1⟩Infinite non-Abelian group
9666⟨a, b | aababaaba=1⟩Infinite non-Abelian group
9699⟨a, b | abaaabaab=1⟩Infinite non-Abelian group1 anti-iso
9700⟨a, b | abaaababa=1⟩Infinite non-Abelian group
101420⟨a, b | aabababaab=1⟩Infinite non-Abelian group3 iso
101491⟨a, b | abaabaaaab=1⟩Infinite non-Abelian group

Solved by frequency:3/2

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9696⟨a, b | abaaaaaba=1⟩Infinite non-Abelian group

Solved by frequency:4/2

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9707⟨a, b | abaabbaab=1⟩Infinite non-Abelian group2 iso

Solved by frequency:4/4

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101476⟨a, b | abaaaaaaba=1⟩Infinite non-Abelian group

Solved by frequency:6/4

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101452⟨a, b | aabbabbaab=1⟩Infinite non-Abelian group2 iso
101516⟨a, b | abababbbba=1⟩Infinite non-Abelian group

Solved by frequency:8/0

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101478⟨a, b | abaaaaabba=1⟩Infinite non-Abelian group

Solved by frequency:8/2

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101431⟨a, b | aababbabba=1⟩Infinite non-Abelian group1 anti-iso

Solved by frequency:9/3

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101457⟨a, b | aabbbaaaab=1⟩Infinite non-Abelian group
101541⟨a, b | abbbaaaaab=1⟩Infinite non-Abelian group

Solved by frequency:9/4

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101466⟨a, b | aabbbbaaab=1⟩Infinite non-Abelian group