#14472 ⟨a, b | aaab=a, bbbbb=b⟩

Properties

Presentation has sum-of-sides 11
Finite non-commutative monoid with 45 elements

Elements

Elements in the center commute with all other elements.
An idempotent element x satisfies x² = x.
The index and period of x is the least m (index) and n (period) such that x^(m+n) = x^m.

1 element center:
- 1
6 non-trivial idempotents:
- ba², b⁴, b²a⁴, a⁸, b³a⁶, b⁴a⁸
Order of generators:
- a: index 1, period 8
- b: index 1, period 4

Histogram:

index 1, period 1	6 elements	ba², b⁴, b²a⁴, a⁸, b³a⁶, ...
index 1, period 2	6 elements	b², a⁴, b³a², ba⁶, b⁴a⁴, ...
index 1, period 4	12 elements	b, a², b³, b²a², ba⁴, ...
index 1, period 8	20 elements	a, ba, a³, b²a, ba³, ...

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

a⁹ ⇒ a
ab ⇒ a⁷
b⁵ ⇒ b

# ab:aaab=a,bbbbb=b a/b
aaaaaaaaa=a
ab=aaaaaaa
bbbbb=b

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#14472 ⟨a, b | aaab=a, bbbbb=b⟩

Properties

Elements

Complete rewriting system

Right Cayley graph

Left Cayley graph