#15372 ⟨a, b | aba=bb, aaabbb=1⟩

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Properties

Elements

Elements in the center commute with all other elements.
The order of x is the least n such that xn = 1.

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. a18 ⇒ 1
  2. a3b ⇒ ba3
  3. b2 ⇒ aba
  4. bab ⇒ a14
  5. ba2b ⇒ a2ba11 
# ab:aba=bb,aaabbb=1 a/b
aaaaaaaaaaaaaaaaaa=1
aaab=baaa
bb=aba
bab=aaaaaaaaaaaaaa
baab=aabaaaaaaaaaaa

Right Cayley graph

Left Cayley graph

Others with same cardinality

1 unique, 3 total

Σ#PresentationDescriptionRelated
1126637⟨a, b | aa=1, abbbbbba=b⟩Finite non-commutative monoid with 72 elements2 iso

Other isomorphic instances

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

2 total

Σ#PresentationMapping
1115378⟨a, b | aba=bb, aabbba=1⟩φ(a) = a, φ(b) = b
1115392⟨a, b | aba=bb, baaabb=1⟩φ(a) = a, φ(b) = b