#43 ⟨a, b, c | ba=ac, bb=1⟩

Up:Monoid enumeration
Prev:#42 ⟨a, b, c | ba=ab, cc=1⟩
Next:#44 ⟨a, b, c | ba=ac, bc=1⟩

Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

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. b2 ⇒ 1 [2]
2. ac ⇒ ba [1]
# abc:ba=ac,bb=1 bac - -
bb=1
ac=ba

Isomorphic instances

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

8 total

Σ#PresentationMapping
6215⟨a, b, c | aa=1, abc=b⟩φ(a) = b, φ(b) = a, φ(c) = c
86619⟨a, b, c | aa=1, aaabc=b⟩φ(a) = b, φ(b) = a, φ(c) = c
86642⟨a, b, c | aa=1, abaac=b⟩φ(a) = b, φ(b) = a, φ(c) = c
87119⟨a, b, c | aa=1, aaab=bc⟩φ(a) = b, φ(b) = a, φ(c) = c
87134⟨a, b, c | aa=1, aabc=ab⟩φ(a) = b, φ(b) = a, φ(c) = c
87201⟨a, b, c | aa=1, baac=ab⟩φ(a) = b, φ(b) = a, φ(c) = c
87623⟨a, b, c | aa=1, abc=aab⟩φ(a) = b, φ(b) = a, φ(c) = c
87634⟨a, b, c | aa=1, baa=abc⟩φ(a) = b, φ(b) = a, φ(c) = c