#11251 ⟨a, b | aaaba=b, bbbbb=1⟩

Properties

Presentation has sum-of-sides 11
Finite non-Abelian group with 1220 elements
Inverses of generators:
- a^-1 = a²⁴³
- b^-1 = b⁴

Element profile

4 element center:
- 1, a⁶¹, a¹²², a¹⁸³

Complete rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1

a²⁴⁴ ⇒ 1
ab ⇒ ba⁸¹
b⁵ ⇒ 1

# ab:aaaba=b,bbbbb=1 a/b
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=1
ab=baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
bbbbb=1

Up:	Monoids with two generators and two relations
Prev:	#11222 ⟨a, b \| aaaba=a, bbbbb=1⟩
Next:	#11253 ⟨a, b \| aaabb=a, aabab=1⟩

#11251 ⟨a, b | aaaba=b, bbbbb=1⟩

Properties

Element profile

Complete rewriting system

Right Cayley graph

Left Cayley graph