#21751 ⟨a, b | aaa=1, abbbbbb=b⟩

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Properties

Element profile

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. b16 ⇒ b
  2. ab ⇒ b11
  3. a3 ⇒ 1 
# ab:aaa=1,abbbbbb=b b/a
bbbbbbbbbbbbbbbb=b
ab=bbbbbbbbbbb
aaa=1

Right Cayley graph

Left Cayley graph

Others with same cardinality

4 unique, 17 total

Σ#PresentationDescriptionRelated
103771⟨a, b | aaaa=bb, abab=1⟩Finite non-Abelian group with 48 elements5 iso
1114993⟨a, b | aaa=bb, ababbb=1⟩Finite non-Abelian group with 48 elements2 iso
1116966⟨a, b | abab=1, aaabbba=1⟩Finite non-Abelian group with 48 elements6 iso
1117503⟨a, b | abab=1, aabbaa=b⟩Finite non-Abelian group with 48 elements

Other isomorphic instances

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

1 total

Σ#PresentationMapping
1122326⟨a, b | aaa=1, bbbbbb=ab⟩φ(a) = a, φ(b) = ba