#7548 ⟨a, b | aaa=1, bbabbb=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. b35 ⇒ 1 [25]
2. ab ⇒ b11a [23]
3. a3 ⇒ 1 [1]
# ab:aaa=1,bbabbb=a reversed:b/a - -
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1
ab=bbbbbbbbbbba
aaa=1

Isomorphic instances

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

5 total

Σ#PresentationMapping
1121170⟨a, b | aaa=1, aabbabbb=1⟩φ(a) = a, φ(b) = b
1121209⟨a, b | aaa=1, abbabbba=1⟩φ(a) = a, φ(b) = b
1121212⟨a, b | aaa=1, abbbaabb=1⟩φ(a) = a, φ(b) = b
1121232⟨a, b | aaa=1, baabbabb=1⟩φ(a) = a, φ(b) = b
1121774⟨a, b | aaa=1, babbabb=a⟩φ(a) = a, φ(b) = ba

Anti-isomorphic instances

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

4 total

Σ#PresentationMapping
1121173⟨a, b | aaa=1, aabbbabb=1⟩φ(a) = a, φ(b) = b
1121205⟨a, b | aaa=1, abbaabbb=1⟩φ(a) = a, φ(b) = b
1121233⟨a, b | aaa=1, baabbbab=1⟩φ(a) = a, φ(b) = b
1121241⟨a, b | aaa=1, babbaabb=1⟩φ(a) = a, φ(b) = b