#5728 ⟨a, b | aaaa=1, babbb=a⟩

Properties

Presentation has sum-of-sides 10
Finite non-Abelian group with 320 elements
Inverses of generators:
- a^-1 = a³
- b^-1 = b⁷⁹

Element profile

4 element center:
- 1, b²⁰, b⁴⁰, b⁶⁰

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(b) = 0; deg(a) = 1

b⁸⁰ ⇒ 1
ba ⇒ ab⁷⁷
a⁴ ⇒ 1

# ab:aaaa=1,babbb=a b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1
ba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
aaaa=1

Up:	Monoids with two generators and two relations
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#5728 ⟨a, b | aaaa=1, babbb=a⟩

Properties

Element profile

Complete rewriting system

Right Cayley graph

Left Cayley graph