〈a, b | aaba=bb, bbbbb=1〉

Monoid presentation of length 11

Properties

Finite non-Abelian group with 165 elements

Completion parameters

Reduction order: left-to-right a/b

Inverses of generators

a^-1 = a¹⁴
b^-1 = aba²ba³

Complete rewriting system

a¹⁵ ⇒ 1
a⁵b ⇒ ba⁵
b² ⇒ a²ba
ba⁴b ⇒ a⁴ba³
(ab)² ⇒ ba³ba¹⁴
aba³b ⇒ (ba²)²
a(a²b)² ⇒ baba⁴
baba²b ⇒ a¹²
b(a²b)² ⇒ a³ba⁷

Right Cayley graph

Left Cayley graph

Others with same cardinality

3 unique, 8 total

Length:	Presentation:	Description:	Related:
10	〈a, b \| aaba=b, bbbbb=1〉	Finite non-Abelian group with 165 elements
11	〈a, b \| aabba=b, bbbbb=1〉	Finite non-Abelian group with 165 elements
11	〈a, b \| aaaaa=1, aababb=1〉	Finite non-Abelian group with 165 elements	3 isomorphic, 2 anti-isomorphic