#16549 ⟨a, b | aba=bb, bab=aaa⟩

Properties

Presentation has sum-of-sides 11
Finite non-commutative monoid with 75 elements

Element profile

5 element center:
- 1, a⁴, a⁸, a¹², a¹⁶
2 idempotent elements:
- 1, a¹⁶

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

a¹⁷ ⇒ a⁹
ba¹⁴ ⇒ ba⁶
a²ba¹¹ ⇒ a²ba³
a³ba¹⁰ ⇒ a³ba²
a⁴b ⇒ ba⁴
b² ⇒ aba
bab ⇒ a³
ba²ba ⇒ a³b
ba³ba⁸ ⇒ ba³b
aba²b ⇒ ba³
aba³b ⇒ ba³ba⁷

# ab:aba=bb,bab=aaa a/b
aaaaaaaaaaaaaaaaa=aaaaaaaaa
baaaaaaaaaaaaaa=baaaaaa
aabaaaaaaaaaaa=aabaaa
aaabaaaaaaaaaa=aaabaa
aaaab=baaaa
bb=aba
bab=aaa
baaba=aaab
baaabaaaaaaaa=baaab
abaab=baaa
abaaab=baaabaaaaaaa

Right Cayley graph

Left Cayley graph

Others with same cardinality

1 unique, 2 total

Σ	#	Presentation	Description	Related
11	13119	⟨a, b \| bbb=aaa, abba=b⟩	Finite non-commutative monoid with 75 elements	1 iso

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