Infinite non-Abelian groups

Up:Monoid enumeration
53 unique, 1102 total

Σ#PresentationPropertiesDescriptionφ
521⟨a, b, c | aa=1, bcb=1⟩Grp Infℤ2 ∗ ℤ225
658⟨a, b, c | aaa=1, bcb=1⟩Grp Infℤ3 ∗ ℤ27
668⟨a, b, c | aab=1, bcc=1⟩Grp Inf294
6175⟨a, b, c | aa=1, bccb=1⟩Grp Inf8
7279⟨a, b, c | aaa=b, cbc=1⟩Grp Inf146
7366⟨a, b, c | aba=b, cbc=1⟩Grp Inf93
7417⟨a, b, c | abc=b, cba=1⟩Grp Inf10
7500⟨a, b, c | bb=ac, bca=1⟩Grp Inf40
7579⟨a, b, c | aaa=1, bccb=1⟩Grp Inf
7679⟨a, b, c | aba=1, cccc=1⟩Grp Infℤ4 ∗ ℤ11
71086⟨a, b, c | aa=1, abccb=1⟩Grp Inf5
71109⟨a, b, c | aa=1, bbccb=1⟩Grp Inf
71112⟨a, b, c | aa=1, bcbbc=1⟩Grp Infℤ2 ∗ ℤ1
71114⟨a, b, c | aa=1, bcccb=1⟩Grp Inf
81577⟨a, b, c | aaa=bb, cac=1⟩Grp Inf22
81578⟨a, b, c | aaa=bb, cbc=1⟩Grp Inf9
81585⟨a, b, c | aaa=bc, acb=1⟩Grp Inf7
81714⟨a, b, c | aab=bc, cba=1⟩Grp Inf38
81782⟨a, b, c | aab=cc, bbc=1⟩Grp Inf1
81997⟨a, b, c | abc=bb, cba=1⟩Grp Inf5
82046⟨a, b, c | aaaa=1, bccb=1⟩Grp Inf
82084⟨a, b, c | aaab=1, bccc=1⟩Grp Inf26
82174⟨a, b, c | aabb=1, acca=1⟩Grp Inf6
82179⟨a, b, c | aabb=1, bacc=1⟩Grp Inf15
82183⟨a, b, c | aabb=1, bcac=1⟩Grp Inf7
82184⟨a, b, c | aabb=1, bcbc=1⟩Grp Inf2
82199⟨a, b, c | aabc=1, acba=1⟩Grp Inf5
82228⟨a, b, c | aabc=1, cbac=1⟩Grp Inf11
82247⟨a, b, c | abab=1, bcbc=1⟩Grp Inf
82272⟨a, b, c | abac=1, caba=1⟩Grp Infℤ ∗ ℤ1
82621⟨a, b, c | aba=b, bccb=1⟩Grp Inf1
83255⟨a, b, c | bb=aa, acca=1⟩Grp Inf
83624⟨a, b, c | aaa=1, abccb=1⟩Grp Inf3
83647⟨a, b, c | aaa=1, bbccb=1⟩Grp Inf
83650⟨a, b, c | aaa=1, bcbbc=1⟩Grp Infℤ3 ∗ ℤ1
83652⟨a, b, c | aaa=1, bcccb=1⟩Grp Inf
83749⟨a, b, c | aab=1, bbcac=1⟩Grp Inf16
83978⟨a, b, c | aba=1, ccccc=1⟩Grp Infℤ5 ∗ ℤ
84476⟨a, b, c | aba=1, cbcc=b⟩Grp Inf
86154⟨a, b, c | aa=1, abaccb=1⟩Grp Inf1
86171⟨a, b, c | aa=1, abbccb=1⟩Grp Inf10
86177⟨a, b, c | aa=1, abcacb=1⟩Grp Inf1
86186⟨a, b, c | aa=1, abccab=1⟩Grp Inf
86222⟨a, b, c | aa=1, bacacb=1⟩Grp Inf
86229⟨a, b, c | aa=1, baccab=1⟩Grp Inf
86251⟨a, b, c | aa=1, bbbccb=1⟩Grp Inf1
86256⟨a, b, c | aa=1, bbcbcb=1⟩Grp Inf
86258⟨a, b, c | aa=1, bbccbb=1⟩Grp Inf
86260⟨a, b, c | aa=1, bbcccb=1⟩Grp Inf
86267⟨a, b, c | aa=1, bcbbbc=1⟩Grp Inf
86268⟨a, b, c | aa=1, bcbbcb=1⟩Grp Inf
86270⟨a, b, c | aa=1, bcbccb=1⟩Grp Inf
86271⟨a, b, c | aa=1, bccbbc=1⟩Grp Inf