#54 ⟨a, b | ab=a, bbb=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. ab ⇒ a
  2. b3 ⇒ 1 
# ab:ab=a,bbb=1 ab
ab=a
bbb=1

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.

12 total

Σ#PresentationMapping
7139⟨a, b | abb=a, bbb=1⟩φ(a) = a, φ(b) = b
8447⟨a, b | abb=ab, bbb=1⟩φ(a) = a, φ(b) = b
92421⟨a, b | aaa=1, aaaba=b⟩φ(a) = b, φ(b) = a
92565⟨a, b | aaa=1, aaab=ba⟩φ(a) = b, φ(b) = a
107489⟨a, b | aaa=1, aaabaa=b⟩φ(a) = b, φ(b) = a
108034⟨a, b | aaa=1, aaab=baa⟩φ(a) = b, φ(b) = a
108039⟨a, b | aaa=1, aaba=aab⟩φ(a) = b, φ(b) = a
1122200⟨a, b | aaa=1, aaaaba=ab⟩φ(a) = b, φ(b) = a
1122209⟨a, b | aaa=1, aaabaa=ba⟩φ(a) = b, φ(b) = a
1122728⟨a, b | aaa=1, aaaab=aba⟩φ(a) = b, φ(b) = a
1122738⟨a, b | aaa=1, aaaba=baa⟩φ(a) = b, φ(b) = a
1122751⟨a, b | aaa=1, aabaa=aab⟩φ(a) = b, φ(b) = a