#16601 ⟨a, b | aaaa=1, ababbbb=1⟩

Properties

Presentation has sum-of-sides 11
Finite non-Abelian group with 480 elements
Inverses of generators:
- a^-1 = bab⁴
- b^-1 = b⁵⁹

Element profile

20 element center:
- 1, b³, b⁶, b⁹, b¹², b¹⁵, b¹⁸, b²¹, b²⁴, b²⁷, b³⁰, b³³, b³⁶, b³⁹, b⁴², b⁴⁵, b⁴⁸, b⁵¹, b⁵⁴, b⁵⁷

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

b⁶⁰ ⇒ 1
b³a ⇒ ab³
aba ⇒ b⁵⁶
bab²a ⇒ a²b⁵³
b²a² ⇒ ab²ab¹⁰
a³ ⇒ bab⁴
ba²b²a ⇒ a²b²ab⁴¹

# ab:aaaa=1,ababbbb=1 b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1
bbba=abbb
aba=bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
babba=aabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
bbaa=abbabbbbbbbbbb
aaa=babbbb
baabba=aabbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Right Cayley graph

Left Cayley graph

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

3 total

Σ	#	Presentation	Mapping
11	16609	⟨a, b \| aaaa=1, abbbbab=1⟩	φ(a) = a, φ(b) = b
11	16622	⟨a, b \| aaaa=1, bababbb=1⟩	φ(a) = a, φ(b) = b
11	16628	⟨a, b \| aaaa=1, bbababb=1⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
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Next:	#16631 ⟨a, b \| aaaa=1, bbbbbbb=1⟩