#17666 ⟨a, b | aaaa=1, abbbb=ba⟩

Properties

Presentation has sum-of-sides 11
Finite non-commutative monoid with 1024 elements

Element profile

4 element center:
- 1, b⁸⁵, b¹⁷⁰, b²⁵⁵
2 idempotent elements:
- 1, b²⁵⁵

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

b²⁵⁶ ⇒ b
ba ⇒ ab⁴
a⁴ ⇒ 1

# ab:aaaa=1,abbbb=ba b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=b
ba=abbbb
aaaa=1

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#17666 ⟨a, b | aaaa=1, abbbb=ba⟩

Properties

Element profile

Complete rewriting system

Right Cayley graph

Left Cayley graph