#14354 ⟨a, b | aaaa=a, abbba=b⟩

Properties

Presentation has sum-of-sides 11
Finite non-commutative monoid with 148 elements

Element profile

8 element center:
- 1, a³, b⁴, b⁸, b¹², b¹⁶, b²⁰, b²⁴
3 idempotent elements:
- 1, a³, b²⁴

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

b²⁵ ⇒ b
bab²⁴ ⇒ ba
b⁴a ⇒ ab⁴
a²b ⇒ b³a
ab²a ⇒ bab²¹
ab³a ⇒ b
ba² ⇒ ab³
(ba)² ⇒ abab⁷
a⁴ ⇒ a

# ab:aaaa=a,abbba=b b/a
bbbbbbbbbbbbbbbbbbbbbbbbb=b
babbbbbbbbbbbbbbbbbbbbbbbb=ba
bbbba=abbbb
aab=bbba
abba=babbbbbbbbbbbbbbbbbbbbb
abbba=b
baa=abbb
baba=ababbbbbbb
aaaa=a

Right Cayley graph

Left Cayley graph

Others with same cardinality

1 unique, 4 total

Σ	#	Presentation	Description	Related
11	10767	⟨a, b \| aaab=bba, bbbb=1⟩	Finite non-commutative monoid with 148 elements	2 iso, 1 anti-iso

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