Infinite non-Abelian groups

Up:Monoids with two generators and two relations
71 unique, 747 total

Σ#PresentationDescriptionRelated
42⟨a, b | aa=1, bb=1⟩Isomorphic to ℤ2 ∗ ℤ2110 iso
516⟨a, b | aa=1, bbb=1⟩Isomorphic to ℤ2 ∗ ℤ3146 iso
628⟨a, b | aaa=1, bbb=1⟩Isomorphic to ℤ3 ∗ ℤ322 iso
668⟨a, b | aa=1, abab=1⟩Infinite non-Abelian group63 iso
673⟨a, b | aa=1, bbbb=1⟩Isomorphic to ℤ2 ∗ ℤ446 iso
7167⟨a, b | aaa=1, abab=1⟩Infinite non-Abelian group28 iso
7172⟨a, b | aaa=1, bbbb=1⟩Isomorphic to ℤ3 ∗ ℤ415 iso
7302⟨a, b | aa=1, bbbbb=1⟩Isomorphic to ℤ2 ∗ ℤ547 iso
8445⟨a, b | aba=bb, bbb=1⟩Infinite non-Abelian group5 iso
8455⟨a, b | aaaa=1, aabb=1⟩Infinite non-Abelian group23 iso
8456⟨a, b | aaaa=1, abab=1⟩Infinite non-Abelian group7 iso
8461⟨a, b | aaaa=1, bbbb=1⟩Isomorphic to ℤ4 ∗ ℤ41 iso
8489⟨a, b | abab=1, baba=1⟩Infinite non-Abelian group1 iso
8562⟨a, b | aba=b, bbbb=1⟩Infinite non-Abelian group4 iso
8683⟨a, b | aaa=1, bbbbb=1⟩Isomorphic to ℤ3 ∗ ℤ57 iso
8750⟨a, b | aaa=1, baab=a⟩Infinite non-Abelian group14 iso
81042⟨a, b | aa=1, ababab=1⟩Infinite non-Abelian group13 iso
81059⟨a, b | aa=1, bbbbbb=1⟩Isomorphic to ℤ2 ∗ ℤ68 iso
91475⟨a, b | aaa=bb, bbbb=1⟩Infinite non-Abelian group7 iso
91707⟨a, b | aaaa=1, aabbb=1⟩Infinite non-Abelian group18 iso
91719⟨a, b | aaaa=1, bbbbb=1⟩Isomorphic to ℤ4 ∗ ℤ52 iso
91800⟨a, b | abab=1, aaaaa=1⟩Infinite non-Abelian group6 iso
92298⟨a, b | aaa=1, ababab=1⟩Infinite non-Abelian group6 iso
92302⟨a, b | aaa=1, abbabb=1⟩Infinite non-Abelian group10 iso
92315⟨a, b | aaa=1, bbbbbb=1⟩Isomorphic to ℤ3 ∗ ℤ62 iso
92452⟨a, b | aaa=1, bbabb=a⟩Infinite non-Abelian group11 iso
93271⟨a, b | aa=1, bbbbbbb=1⟩Isomorphic to ℤ2 ∗ ℤ78 iso
103770⟨a, b | aaaa=bb, aabb=1⟩Infinite non-Abelian group5 iso
103776⟨a, b | aaaa=bb, bbbb=1⟩Infinite non-Abelian group
103911⟨a, b | aabb=ba, baba=1⟩Infinite non-Abelian group3 iso
103940⟨a, b | abab=ba, abba=1⟩Infinite non-Abelian group4 iso
103977⟨a, b | abba=bb, bbbb=1⟩Infinite non-Abelian group
104218⟨a, b | aaaaa=1, bbbbb=1⟩Isomorphic to ℤ5 ∗ ℤ5
105427⟨a, b | aaaa=1, aaabab=1⟩Infinite non-Abelian group2 iso
105430⟨a, b | aaaa=1, aabaab=1⟩Infinite non-Abelian group1 iso
105436⟨a, b | aaaa=1, aabbbb=1⟩Infinite non-Abelian group3 iso
105440⟨a, b | aaaa=1, ababab=1⟩Infinite non-Abelian group
105444⟨a, b | aaaa=1, abbabb=1⟩Infinite non-Abelian group1 iso
105457⟨a, b | aaaa=1, bbbbbb=1⟩Isomorphic to ℤ4 ∗ ℤ6
105622⟨a, b | abab=1, aaaaaa=1⟩Infinite non-Abelian group
105722⟨a, b | aaaa=1, baaab=a⟩Infinite non-Abelian group
105726⟨a, b | aaaa=1, babab=a⟩Infinite non-Abelian group
106237⟨a, b | aba=b, bbbbbb=1⟩Infinite non-Abelian group
106930⟨a, b | bb=aa, aaaaaa=1⟩Infinite non-Abelian group6 iso
107279⟨a, b | aaa=1, bbbbbbb=1⟩Isomorphic to ℤ3 ∗ ℤ7
109456⟨a, b | aa=1, abababab=1⟩Infinite non-Abelian group1 iso
109474⟨a, b | aa=1, abbabbbb=1⟩Infinite non-Abelian group5 iso
109519⟨a, b | aa=1, bbbbbbbb=1⟩Isomorphic to ℤ2 ∗ ℤ8
1111343⟨a, b | aabaa=b, bbbbb=1⟩Infinite non-Abelian group
1113281⟨a, b | aaaaa=1, aabaab=1⟩Infinite non-Abelian group1 iso
1113291⟨a, b | aaaaa=1, ababab=1⟩Infinite non-Abelian group
1113295⟨a, b | aaaaa=1, abbabb=1⟩Infinite non-Abelian group1 iso
1113308⟨a, b | aaaaa=1, bbbbbb=1⟩Isomorphic to ℤ5 ∗ ℤ6
1113500⟨a, b | aaabb=1, bbbbbb=1⟩Infinite non-Abelian group1 iso
1113765⟨a, b | abbba=1, aaaaaa=1⟩Infinite non-Abelian group
1114298⟨a, b | abba=b, aaabab=1⟩Infinite non-Abelian group2 iso
1114301⟨a, b | abba=b, aabaab=1⟩Infinite non-Abelian group1 iso
1114328⟨a, b | abba=b, bbbbbb=1⟩Infinite non-Abelian group
1115008⟨a, b | aaa=bb, bbbbbb=1⟩Infinite non-Abelian group
1115400⟨a, b | aba=bb, bbbbbb=1⟩Infinite non-Abelian group
1116578⟨a, b | aaaa=1, aabaabb=1⟩Infinite non-Abelian group4 iso
1116589⟨a, b | aaaa=1, aabbbbb=1⟩Infinite non-Abelian group4 iso
1116631⟨a, b | aaaa=1, bbbbbbb=1⟩Isomorphic to ℤ4 ∗ ℤ7
1116952⟨a, b | abab=1, aaaaaaa=1⟩Infinite non-Abelian group
1121192⟨a, b | aaa=1, abababab=1⟩Infinite non-Abelian group
1121214⟨a, b | aaa=1, abbbabbb=1⟩Infinite non-Abelian group1 iso
1121255⟨a, b | aaa=1, bbbbbbbb=1⟩Isomorphic to ℤ3 ∗ ℤ8
1121760⟨a, b | aaa=1, baabaab=a⟩Infinite non-Abelian group
1121786⟨a, b | aaa=1, bbabbbb=a⟩Infinite non-Abelian group
1121788⟨a, b | aaa=1, bbbabbb=a⟩Infinite non-Abelian group
1126183⟨a, b | aa=1, bbbbbbbbb=1⟩Isomorphic to ℤ2 ∗ ℤ9