#7544 ⟨a, b | aaa=1, babbbb=a⟩

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Contents

  1. Properties
  2. Finite structure
  3. Right Cayley graph
  4. Left Cayley graph
  5. Rewriting system
  6. Isomorphic instances
  7. Anti-isomorphic instances

Properties

Finite structure

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

Right Cayley graph

Left Cayley graph

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. b65 ⇒ 1 [33]
2. ab ⇒ b16a [31]
3. a3 ⇒ 1 [1]
# ab:aaa=1,babbbb=a reversed:b/a - -
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1
ab=bbbbbbbbbbbbbbbba
aaa=1

Isomorphic instances

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

5 total

Σ#PresentationMapping
1121164⟨a, b | aaa=1, aababbbb=1⟩φ(a) = a, φ(b) = b
1121199⟨a, b | aaa=1, ababbbba=1⟩φ(a) = a, φ(b) = b
1121215⟨a, b | aaa=1, abbbbaab=1⟩φ(a) = a, φ(b) = b
1121230⟨a, b | aaa=1, baababbb=1⟩φ(a) = a, φ(b) = b
1121248⟨a, b | aaa=1, bbaababb=1⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

3 total

Σ#PresentationMapping
1121175⟨a, b | aaa=1, aabbbbab=1⟩φ(a) = a, φ(b) = b
1121189⟨a, b | aaa=1, abaabbbb=1⟩φ(a) = a, φ(b) = b
1121237⟨a, b | aaa=1, babaabbb=1⟩φ(a) = a, φ(b) = b