Infinite non-Abelian groups

Up:Monoid enumeration
79 unique, 812 total

Σ#PresentationPropertiesDescriptionφ
42⟨a, b | aa=1, bb=1⟩Grp Infℤ2 ∗ ℤ2110
516⟨a, b | aa=1, bbb=1⟩Grp Infℤ2 ∗ ℤ3146
628⟨a, b | aaa=1, bbb=1⟩Grp Infℤ3 ∗ ℤ322
668⟨a, b | aa=1, abab=1⟩Grp Inf63
673⟨a, b | aa=1, bbbb=1⟩Grp Infℤ2 ∗ ℤ446
7167⟨a, b | aaa=1, abab=1⟩Grp Inf28
7172⟨a, b | aaa=1, bbbb=1⟩Grp Infℤ3 ∗ ℤ415
7302⟨a, b | aa=1, bbbbb=1⟩Grp Infℤ2 ∗ ℤ547
8445⟨a, b | aba=bb, bbb=1⟩Grp Inf5
8455⟨a, b | aaaa=1, aabb=1⟩Grp Inf23
8456⟨a, b | aaaa=1, abab=1⟩Grp Inf7
8461⟨a, b | aaaa=1, bbbb=1⟩Grp Infℤ4 ∗ ℤ41
8485⟨a, b | aabb=1, abba=1⟩Grp Inf14
8489⟨a, b | abab=1, baba=1⟩Grp Inf1
8562⟨a, b | aba=b, bbbb=1⟩Grp Inf4
8683⟨a, b | aaa=1, bbbbb=1⟩Grp Infℤ3 ∗ ℤ57
8750⟨a, b | aaa=1, baab=a⟩Grp Inf14
81042⟨a, b | aa=1, ababab=1⟩Grp Inf13
81046⟨a, b | aa=1, abbabb=1⟩Grp Inf24
81059⟨a, b | aa=1, bbbbbb=1⟩Grp Infℤ2 ∗ ℤ68
91475⟨a, b | aaa=bb, bbbb=1⟩Grp Inf7
91707⟨a, b | aaaa=1, aabbb=1⟩Grp Inf18
91719⟨a, b | aaaa=1, bbbbb=1⟩Grp Infℤ4 ∗ ℤ52
91800⟨a, b | abab=1, aaaaa=1⟩Grp Inf6
92298⟨a, b | aaa=1, ababab=1⟩Grp Inf6
92302⟨a, b | aaa=1, abbabb=1⟩Grp Inf10
92315⟨a, b | aaa=1, bbbbbb=1⟩Grp Infℤ3 ∗ ℤ62
92452⟨a, b | aaa=1, bbabb=a⟩Grp Inf13
93271⟨a, b | aa=1, bbbbbbb=1⟩Grp Infℤ2 ∗ ℤ78
103770⟨a, b | aaaa=bb, aabb=1⟩Grp Inf5
103776⟨a, b | aaaa=bb, bbbb=1⟩Grp Inf
103911⟨a, b | aabb=ba, baba=1⟩Grp Inf3
103940⟨a, b | abab=ba, abba=1⟩Grp Inf4
103977⟨a, b | abba=bb, bbbb=1⟩Grp Inf
104084⟨a, b | baa=aab, abab=1⟩Grp Inf1
104218⟨a, b | aaaaa=1, bbbbb=1⟩Grp Infℤ5 ∗ ℤ5
104275⟨a, b | aaabb=1, aabba=1⟩Grp Inf8
105427⟨a, b | aaaa=1, aaabab=1⟩Grp Inf2
105430⟨a, b | aaaa=1, aabaab=1⟩Grp Inf1
105436⟨a, b | aaaa=1, aabbbb=1⟩Grp Inf3
105440⟨a, b | aaaa=1, ababab=1⟩Grp Inf
105444⟨a, b | aaaa=1, abbabb=1⟩Grp Inf1
105457⟨a, b | aaaa=1, bbbbbb=1⟩Grp Infℤ4 ∗ ℤ6
105622⟨a, b | abab=1, aaaaaa=1⟩Grp Inf
105722⟨a, b | aaaa=1, baaab=a⟩Grp Inf
105726⟨a, b | aaaa=1, babab=a⟩Grp Inf
105730⟨a, b | aaaa=1, bbabb=a⟩Grp Inf
105903⟨a, b | abab=1, aabaa=b⟩Grp Inf
106237⟨a, b | aba=b, bbbbbb=1⟩Grp Inf
106930⟨a, b | bb=aa, aaaaaa=1⟩Grp Inf6
107279⟨a, b | aaa=1, bbbbbbb=1⟩Grp Infℤ3 ∗ ℤ7
107546⟨a, b | aaa=1, bbaabb=a⟩Grp Inf3
109456⟨a, b | aa=1, abababab=1⟩Grp Inf1
109474⟨a, b | aa=1, abbabbbb=1⟩Grp Inf5
109478⟨a, b | aa=1, abbbabbb=1⟩Grp Inf2
109519⟨a, b | aa=1, bbbbbbbb=1⟩Grp Infℤ2 ∗ ℤ8
1111343⟨a, b | aabaa=b, bbbbb=1⟩Grp Inf
1113281⟨a, b | aaaaa=1, aabaab=1⟩Grp Inf1
1113291⟨a, b | aaaaa=1, ababab=1⟩Grp Inf
1113295⟨a, b | aaaaa=1, abbabb=1⟩Grp Inf1
1113308⟨a, b | aaaaa=1, bbbbbb=1⟩Grp Infℤ5 ∗ ℤ6
1113500⟨a, b | aaabb=1, bbbbbb=1⟩Grp Inf2
1114298⟨a, b | abba=b, aaabab=1⟩Grp Inf2
1114301⟨a, b | abba=b, aabaab=1⟩Grp Inf1
1114328⟨a, b | abba=b, bbbbbb=1⟩Grp Inf
1115008⟨a, b | aaa=bb, bbbbbb=1⟩Grp Inf
1115400⟨a, b | aba=bb, bbbbbb=1⟩Grp Inf
1116578⟨a, b | aaaa=1, aabaabb=1⟩Grp Inf4
1116589⟨a, b | aaaa=1, aabbbbb=1⟩Grp Inf4
1116631⟨a, b | aaaa=1, bbbbbbb=1⟩Grp Infℤ4 ∗ ℤ7
1116952⟨a, b | abab=1, aaaaaaa=1⟩Grp Inf
1121192⟨a, b | aaa=1, abababab=1⟩Grp Inf
1121214⟨a, b | aaa=1, abbbabbb=1⟩Grp Inf1
1121255⟨a, b | aaa=1, bbbbbbbb=1⟩Grp Infℤ3 ∗ ℤ8
1121760⟨a, b | aaa=1, baabaab=a⟩Grp Inf
1121786⟨a, b | aaa=1, bbabbbb=a⟩Grp Inf
1121788⟨a, b | aaa=1, bbbabbb=a⟩Grp Inf
1126090⟨a, b | aa=1, abbabbabb=1⟩Grp Inf2
1126183⟨a, b | aa=1, bbbbbbbbb=1⟩Grp Infℤ2 ∗ ℤ9