Finite Abelian groups

Up:Monoid enumeration
23 unique, 13859 total

Σ#PresentationPropertiesDescriptionφ
41⟨a, b | aa=1, ab=1⟩Grp Com 2ℤ21990
54⟨a, b | aa=a, ab=1⟩Grp Com 1ℤ12030
56⟨a, b | aa=b, ab=1⟩Grp Com 3ℤ32029
57⟨a, b | aa=b, bb=1⟩Grp Com 4ℤ41419
626⟨a, b | aaa=1, abb=1⟩Grp Com 6ℤ61373
644⟨a, b | aa=b, abb=1⟩Grp Com 5ℤ51132
7116⟨a, b | aaa=b, abb=1⟩Grp Com 7ℤ7763
7118⟨a, b | aaa=b, bbb=1⟩Grp Com 9ℤ9562
7188⟨a, b | aab=1, bbbb=1⟩Grp Com 8ℤ8727
8458⟨a, b | aaaa=1, abbb=1⟩Grp Com 12ℤ12325
8507⟨a, b | aaa=b, abbb=1⟩Grp Com 10ℤ10536
91328⟨a, b | aaaa=b, abbb=1⟩Grp Com 13ℤ13189
91331⟨a, b | aaaa=b, bbbb=1⟩Grp Com 16ℤ1667
91472⟨a, b | aaa=bb, abbb=1⟩Grp Com 11ℤ11259
91751⟨a, b | aaab=1, bbbbb=1⟩Grp Com 15ℤ15138
103773⟨a, b | aaaa=bb, abbb=1⟩Grp Com 14ℤ14165
104212⟨a, b | aaaaa=1, abbbb=1⟩Grp Com 20ℤ2016
104375⟨a, b | aaaa=b, abbbb=1⟩Grp Com 17ℤ1739
105521⟨a, b | aaab=1, bbbbbb=1⟩Grp Com 18ℤ1833
1111127⟨a, b | aaaaa=b, abbbb=1⟩Grp Com 21ℤ2113
1111133⟨a, b | aaaaa=b, bbbbb=1⟩Grp Com 25ℤ253
1113340⟨a, b | aaaab=1, abbbbb=1⟩Grp Com 19ℤ1920
1113372⟨a, b | aaaab=1, bbbbbb=1⟩Grp Com 24ℤ248