Infinite non-Abelian groups, two auxiliary generators

Up:Monoids with two generators and one relation

153 unique, 289 total

Solved by magic:0

Σ#PresentationDescriptionRelated
414⟨a, b | abba=1⟩Infinite non-Abelian group
530⟨a, b | aabba=1⟩Infinite non-Abelian group
533⟨a, b | abbba=1⟩Infinite non-Abelian group
660⟨a, b | aaabba=1⟩Infinite non-Abelian group1 iso
663⟨a, b | aababa=1⟩Infinite non-Abelian group1 iso
667⟨a, b | aabbba=1⟩Infinite non-Abelian group
673⟨a, b | abbbba=1⟩Infinite non-Abelian group
7131⟨a, b | aaaabba=1⟩Infinite non-Abelian group1 iso
7135⟨a, b | aaababa=1⟩Infinite non-Abelian group2 iso
7139⟨a, b | aaabbba=1⟩Infinite non-Abelian group1 iso
7145⟨a, b | aababba=1⟩Infinite non-Abelian group2 anti-iso
7146⟨a, b | aabbaab=1⟩Infinite non-Abelian group1 iso
7150⟨a, b | aabbbba=1⟩Infinite non-Abelian group
7158⟨a, b | abbaaab=1⟩Infinite non-Abelian group
7159⟨a, b | abbabba=1⟩Infinite non-Abelian group
7160⟨a, b | abbbbba=1⟩Infinite non-Abelian group
8275⟨a, b | aaaaabba=1⟩Infinite non-Abelian group2 iso
8279⟨a, b | aaaababa=1⟩Infinite non-Abelian group2 iso
8283⟨a, b | aaaabbba=1⟩Infinite non-Abelian group1 iso
8286⟨a, b | aaabaaba=1⟩Infinite non-Abelian group3 iso
8290⟨a, b | aaababba=1⟩Infinite non-Abelian group1 iso, 2 anti-iso
8298⟨a, b | aaabbbba=1⟩Infinite non-Abelian group1 iso
8304⟨a, b | aabaabba=1⟩Infinite non-Abelian group1 iso, 2 anti-iso
8306⟨a, b | aabababa=1⟩Infinite non-Abelian group1 iso
8310⟨a, b | aababbba=1⟩Infinite non-Abelian group1 anti-iso
8320⟨a, b | aabbbbba=1⟩Infinite non-Abelian group
8323⟨a, b | abaaabab=1⟩Infinite non-Abelian group
8335⟨a, b | abbaaaab=1⟩Infinite non-Abelian group
8336⟨a, b | abbaabba=1⟩Infinite non-Abelian group
8339⟨a, b | abbbaaab=1⟩Infinite non-Abelian group
8340⟨a, b | abbbbbba=1⟩Infinite non-Abelian group
9601⟨a, b | aaaaaabba=1⟩Infinite non-Abelian group2 iso
9605⟨a, b | aaaaababa=1⟩Infinite non-Abelian group3 iso
9609⟨a, b | aaaaabbba=1⟩Infinite non-Abelian group2 iso
9613⟨a, b | aaaabaaba=1⟩Infinite non-Abelian group2 iso
9617⟨a, b | aaaababba=1⟩Infinite non-Abelian group1 iso, 3 anti-iso
9625⟨a, b | aaaabbbba=1⟩Infinite non-Abelian group1 iso
9635⟨a, b | aaabababa=1⟩Infinite non-Abelian group2 iso, 1 anti-iso
9639⟨a, b | aaababbba=1⟩Infinite non-Abelian group1 iso, 1 anti-iso
9640⟨a, b | aaabbaaab=1⟩Infinite non-Abelian group2 iso
9652⟨a, b | aaabbbbba=1⟩Infinite non-Abelian group1 iso
9664⟨a, b | aabaabbba=1⟩Infinite non-Abelian group2 anti-iso
9670⟨a, b | aabababba=1⟩Infinite non-Abelian group1 iso, 2 anti-iso
9672⟨a, b | aababbaba=1⟩Infinite non-Abelian group2 iso
9675⟨a, b | aababbbba=1⟩Infinite non-Abelian group1 anti-iso
9678⟨a, b | aabbaaabb=1⟩Infinite non-Abelian group1 anti-iso
9685⟨a, b | aabbabbba=1⟩Infinite non-Abelian group1 anti-iso
9694⟨a, b | aabbbbbba=1⟩Infinite non-Abelian group
9721⟨a, b | abbaaaaab=1⟩Infinite non-Abelian group
9728⟨a, b | abbbaaaab=1⟩Infinite non-Abelian group
9729⟨a, b | abbbabbba=1⟩Infinite non-Abelian group
9730⟨a, b | abbbbbbba=1⟩Infinite non-Abelian group
101281⟨a, b | aaaaaaabba=1⟩Infinite non-Abelian group3 iso
101285⟨a, b | aaaaaababa=1⟩Infinite non-Abelian group1 iso, 1 anti-iso
101289⟨a, b | aaaaaabbba=1⟩Infinite non-Abelian group2 iso
101293⟨a, b | aaaaabaaba=1⟩Infinite non-Abelian group2 iso
101297⟨a, b | aaaaababba=1⟩Infinite non-Abelian group2 iso, 3 anti-iso
101305⟨a, b | aaaaabbbba=1⟩Infinite non-Abelian group2 iso
101308⟨a, b | aaaabaaaba=1⟩Infinite non-Abelian group2 iso
101312⟨a, b | aaaabaabba=1⟩Infinite non-Abelian group1 iso, 3 anti-iso
101314⟨a, b | aaaababaaa=1⟩Infinite non-Abelian group
101316⟨a, b | aaaabababa=1⟩Infinite non-Abelian group1 iso
101320⟨a, b | aaaababbba=1⟩Infinite non-Abelian group1 iso, 2 anti-iso
101336⟨a, b | aaaabbbbba=1⟩Infinite non-Abelian group1 iso
101342⟨a, b | aaabaaabba=1⟩Infinite non-Abelian group3 iso, 2 anti-iso
101351⟨a, b | aaababaaab=1⟩Infinite non-Abelian group1 iso
101356⟨a, b | aaabababba=1⟩Infinite non-Abelian group1 iso, 1 anti-iso
101360⟨a, b | aaababbaba=1⟩Infinite non-Abelian group2 iso
101364⟨a, b | aaababbbba=1⟩Infinite non-Abelian group1 iso, 1 anti-iso
101370⟨a, b | aaabbaabba=1⟩Infinite non-Abelian group1 anti-iso
101377⟨a, b | aaabbabbba=1⟩Infinite non-Abelian group2 iso, 2 anti-iso
101390⟨a, b | aaabbbbbba=1⟩Infinite non-Abelian group1 iso
101391⟨a, b | aabaaaaaab=1⟩Infinite non-Abelian group
101398⟨a, b | aabaaababa=1⟩Infinite non-Abelian group
101409⟨a, b | aabaabbaab=1⟩Infinite non-Abelian group3 iso
101416⟨a, b | aababaaaba=1⟩Infinite non-Abelian group
101421⟨a, b | aababababa=1⟩Infinite non-Abelian group1 anti-iso
101433⟨a, b | aababbbaba=1⟩Infinite non-Abelian group
101436⟨a, b | aababbbbba=1⟩Infinite non-Abelian group1 anti-iso
101437⟨a, b | aabbaaaaab=1⟩Infinite non-Abelian group
101441⟨a, b | aabbaaabba=1⟩Infinite non-Abelian group
101446⟨a, b | aabbaabbba=1⟩Infinite non-Abelian group1 iso, 1 anti-iso
101451⟨a, b | aabbababba=1⟩Infinite non-Abelian group
101474⟨a, b | aabbbbbbba=1⟩Infinite non-Abelian group
101477⟨a, b | abaaaaabab=1⟩Infinite non-Abelian group
101505⟨a, b | ababaaaaab=1⟩Infinite non-Abelian group
101506⟨a, b | ababaaabab=1⟩Infinite non-Abelian group1 iso
101527⟨a, b | abbaaaaaab=1⟩Infinite non-Abelian group
101534⟨a, b | abbaabbbba=1⟩Infinite non-Abelian group
101539⟨a, b | abbabbabba=1⟩Infinite non-Abelian group
101542⟨a, b | abbbaabbba=1⟩Infinite non-Abelian group
101546⟨a, b | abbbbbbbba=1⟩Infinite non-Abelian group

Solved by magic:1

Σ#PresentationDescriptionRelated
8338⟨a, b | abbabbba=1⟩Infinite non-Abelian group
9686⟨a, b | aabbbaaab=1⟩Infinite non-Abelian group
9718⟨a, b | ababbbaab=1⟩Infinite non-Abelian group
9722⟨a, b | abbaaabba=1⟩Infinite non-Abelian group1 iso
101350⟨a, b | aaabaabbba=1⟩Infinite non-Abelian group2 iso, 2 anti-iso
101439⟨a, b | aabbaaaabb=1⟩Infinite non-Abelian group1 iso
101453⟨a, b | aabbabbaba=1⟩Infinite non-Abelian group
101482⟨a, b | abaaaabbba=1⟩Infinite non-Abelian group
101490⟨a, b | abaaabbbba=1⟩Infinite non-Abelian group
101510⟨a, b | ababaabbba=1⟩Infinite non-Abelian group
101524⟨a, b | ababbbbaab=1⟩Infinite non-Abelian group
101525⟨a, b | ababbbbaba=1⟩Infinite non-Abelian group
101544⟨a, b | abbbabbbba=1⟩Infinite non-Abelian group

Solved by frequency:2/0,2/0

Σ#PresentationDescriptionRelated
8332⟨a, b | ababbaab=1⟩Infinite non-Abelian group

Solved by frequency:2/0,2/1

Σ#PresentationDescriptionRelated
671⟨a, b | ababba=1⟩Infinite non-Abelian group1 iso
101518⟨a, b | ababbaabab=1⟩Infinite non-Abelian group
101519⟨a, b | ababbaabba=1⟩Infinite non-Abelian group1 iso

Solved by frequency:2/0,2/2

Σ#PresentationDescriptionRelated
8331⟨a, b | abababba=1⟩Infinite non-Abelian group
101513⟨a, b | ababababba=1⟩Infinite non-Abelian group
101532⟨a, b | abbaababba=1⟩Infinite non-Abelian group

Solved by frequency:2/0,3/0

Σ#PresentationDescriptionRelated
8315⟨a, b | aabbabba=1⟩Infinite non-Abelian group
8316⟨a, b | aabbbaab=1⟩Infinite non-Abelian group
8328⟨a, b | abaabbba=1⟩Infinite non-Abelian group
101515⟨a, b | abababbaba=1⟩Infinite non-Abelian group
101520⟨a, b | ababbabaab=1⟩Infinite non-Abelian group

Solved by frequency:2/0,3/1

Σ#PresentationDescriptionRelated
8333⟨a, b | ababbaba=1⟩Infinite non-Abelian group

Solved by frequency:2/0,3/2

Σ#PresentationDescriptionRelated
9645⟨a, b | aaabbabba=1⟩Infinite non-Abelian group2 iso, 1 anti-iso

Solved by frequency:2/0,3/3

Σ#PresentationDescriptionRelated
101514⟨a, b | abababbaab=1⟩Infinite non-Abelian group

Solved by frequency:2/0,4/0

Σ#PresentationDescriptionRelated
101346⟨a, b | aaabaababa=1⟩Infinite non-Abelian group2 iso, 1 anti-iso

Solved by frequency:2/0,4/4

Σ#PresentationDescriptionRelated
8337⟨a, b | abbabaab=1⟩Infinite non-Abelian group

Solved by frequency:2/0,5/0

Σ#PresentationDescriptionRelated
101352⟨a, b | aaababaaba=1⟩Infinite non-Abelian group
101415⟨a, b | aababaaaab=1⟩Infinite non-Abelian group

Solved by frequency:2/0,5/4

Σ#PresentationDescriptionRelated
101536⟨a, b | abbababaab=1⟩Infinite non-Abelian group

Solved by frequency:2/1,3/1

Σ#PresentationDescriptionRelated
101328⟨a, b | aaaabbabba=1⟩Infinite non-Abelian group

Solved by frequency:2/1,3/2

Σ#PresentationDescriptionRelated
101375⟨a, b | aaabbabbaa=1⟩Infinite non-Abelian group1 anti-iso

Solved by frequency:2/1,3/3

Σ#PresentationDescriptionRelated
101470⟨a, b | aabbbbbaab=1⟩Infinite non-Abelian group

Solved by frequency:2/1,4/0

Σ#PresentationDescriptionRelated
101378⟨a, b | aaabbbaaab=1⟩Infinite non-Abelian group1 anti-iso
101458⟨a, b | aabbbaaaba=1⟩Infinite non-Abelian group

Solved by frequency:2/1,4/5

Σ#PresentationDescriptionRelated
101408⟨a, b | aabaababba=1⟩Infinite non-Abelian group1 iso

Solved by frequency:2/1,5/1

Σ#PresentationDescriptionRelated
9681⟨a, b | aabbabaab=1⟩Infinite non-Abelian group

Solved by frequency:2/2,4/1

Σ#PresentationDescriptionRelated
101402⟨a, b | aabaaabbba=1⟩Infinite non-Abelian group

Solved by frequency:2/2,4/3

Σ#PresentationDescriptionRelated
101448⟨a, b | aabbabaaba=1⟩Infinite non-Abelian group1 anti-iso

Solved by frequency:2/2,5/3

Σ#PresentationDescriptionRelated
101488⟨a, b | abaaabbaba=1⟩Infinite non-Abelian group

Solved by frequency:2/3,2/0

Σ#PresentationDescriptionRelated
9717⟨a, b | ababbabba=1⟩Infinite non-Abelian group

Solved by frequency:2/3,2/2

Σ#PresentationDescriptionRelated
9727⟨a, b | abbabbbba=1⟩Infinite non-Abelian group

Solved by frequency:2/3,3/1

Σ#PresentationDescriptionRelated
9706⟨a, b | abaababba=1⟩Infinite non-Abelian group1 iso, 1 anti-iso

Solved by frequency:2/3,4/3

Σ#PresentationDescriptionRelated
101447⟨a, b | aabbabaaab=1⟩Infinite non-Abelian group1 iso

Solved by frequency:2/3,5/1

Σ#PresentationDescriptionRelated
101521⟨a, b | ababbabbba=1⟩Infinite non-Abelian group

Solved by frequency:2/3,5/2

Σ#PresentationDescriptionRelated
101427⟨a, b | aababbaaba=1⟩Infinite non-Abelian group1 iso
101531⟨a, b | abbaabaaab=1⟩Infinite non-Abelian group

Solved by frequency:3/0,3/0

Σ#PresentationDescriptionRelated
9676⟨a, b | aabbaaaab=1⟩Infinite non-Abelian group

Solved by frequency:3/0,3/2

Σ#PresentationDescriptionRelated
9631⟨a, b | aaabaabba=1⟩Infinite non-Abelian group

Solved by frequency:3/0,3/3

Σ#PresentationDescriptionRelated
9662⟨a, b | aabaabbaa=1⟩Infinite non-Abelian group1 anti-iso
101410⟨a, b | aabaabbaba=1⟩Infinite non-Abelian group

Solved by frequency:3/0,3/4

Σ#PresentationDescriptionRelated
9660⟨a, b | aabaababa=1⟩Infinite non-Abelian group

Solved by frequency:3/0,4/0

Σ#PresentationDescriptionRelated
9671⟨a, b | aababbaab=1⟩Infinite non-Abelian group

Solved by frequency:3/0,4/1

Σ#PresentationDescriptionRelated
9641⟨a, b | aaabbaaba=1⟩Infinite non-Abelian group

Solved by frequency:3/4,3/0

Σ#PresentationDescriptionRelated
101503⟨a, b | abaabbbaba=1⟩Infinite non-Abelian group1 anti-iso

Solved by frequency:5/0,3/0

Σ#PresentationDescriptionRelated
101419⟨a, b | aababaabba=1⟩Infinite non-Abelian group
101443⟨a, b | aabbaababa=1⟩Infinite non-Abelian group1 anti-iso

Solved by frequency:5/3,5/0

Σ#PresentationDescriptionRelated
101487⟨a, b | abaaabbaab=1⟩Infinite non-Abelian group