#69 ⟨a, b | abaaba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Isomorphic instances

Properties

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
#RuleProof
1. ba2ba ⇒ aba2b [2]
2. (a2b)2 ⇒ 1 [4]
# ab:abaaba=1 ab
baaba=abaab
aabaab=1

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
21⟨a, b | aa=1⟩Isomorphic to ℤ2 ∗ ℕ

Isomorphic instances

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

5 total

Σ#PresentationMapping
8300⟨a, b | aabaaaba=1⟩φ(a) = a, φ(b) = abaababaababaabaab
101338⟨a, b | aaabaaaaba=1⟩φ(a) = a, φ(b) = abaababaababaababaabaab
101394⟨a, b | aabaaaabaa=1⟩φ(a) = a, φ(b) = abaababaababaabaababaab
101494⟨a, b | abaababaab=1⟩φ(a) = abaababaabaab, φ(b) = aabaabaabaaabaabaa
101509⟨a, b | ababaababa=1⟩φ(a) = abaababaababa, φ(b) = aabaabaabaaabaabaa