#11787 ⟨a, b | aaab=ba, bbbbb=1⟩

Properties

Presentation has sum-of-sides 11
Finite non-commutative monoid with 1215 elements

Element profile

3 element center:
- 1, a¹²¹, a²⁴²
2 idempotent elements:
- 1, a²⁴²

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:
- Right-to-left recursive path with deg(a) = 0; deg(b) = 1

a²⁴³ ⇒ a
ba ⇒ a³b
b⁵ ⇒ 1

# ab:aaab=ba,bbbbb=1 reversed:a/b
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=a
ba=aaab
bbbbb=1

Up:	Monoids with two generators and two relations
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Next:	#11851 ⟨a, b \| aaba=aa, bbbbb=1⟩

#11787 ⟨a, b | aaab=ba, bbbbb=1⟩

Properties

Element profile

Complete rewriting system

Right Cayley graph

Left Cayley graph