#2298 ⟨a, b | aaa=1, ababab=1⟩

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Properties

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. a3 ⇒ 1
  2. b(ab)2 ⇒ a2 
# ab:aaa=1,ababab=1 ab
aaa=1
babab=aa

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

6 total

Σ#PresentationMapping
107811⟨a, b | aaa=1, babab=aa⟩φ(a) = a, φ(b) = b
1113819⟨a, b | aaaa=a, ababab=1⟩φ(a) = a, φ(b) = b
1113958⟨a, b | aaab=b, ababab=1⟩φ(a) = a, φ(b) = b
1113979⟨a, b | aaab=b, bababa=1⟩φ(a) = a, φ(b) = b
1121688⟨a, b | aaa=1, aababab=a⟩φ(a) = a, φ(b) = b
1121722⟨a, b | aaa=1, abababa=a⟩φ(a) = a, φ(b) = b