#13293 ⟨a, b | aaaaa=1, ababbb=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. b20 ⇒ 1
  2. b2a ⇒ ab2
  3. aba ⇒ b17
  4. a3 ⇒ ba2b7 
# ab:aaaaa=1,ababbb=1 b/a
bbbbbbbbbbbbbbbbbbbb=1
bba=abb
aba=bbbbbbbbbbbbbbbbb
aaa=baabbbbbbb

Right Cayley graph

Left Cayley graph

Others with same cardinality

1 unique, 10 total

Σ#PresentationDescriptionRelated
91434⟨a, b | baab=a, bbbb=1⟩Finite non-commutative monoid with 100 elements9 iso

Other isomorphic instances

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

2 total

Σ#PresentationMapping
1113296⟨a, b | aaaaa=1, abbbab=1⟩φ(a) = a, φ(b) = b
1113303⟨a, b | aaaaa=1, bababb=1⟩φ(a) = a, φ(b) = b