#167 ⟨a, b | aaa=1, abab=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. bab ⇒ a2 
# ab:aaa=1,abab=1 ab
aaa=1
bab=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.

28 total

Σ#PresentationMapping
91317⟨a, b | aaaa=a, abab=1⟩φ(a) = a, φ(b) = b
91349⟨a, b | aaab=b, abab=1⟩φ(a) = a, φ(b) = b
91354⟨a, b | aaab=b, baba=1⟩φ(a) = a, φ(b) = b
92426⟨a, b | aaa=1, aabab=a⟩φ(a) = a, φ(b) = b
92434⟨a, b | aaa=1, ababa=a⟩φ(a) = a, φ(b) = b
107213⟨a, b | aaa=1, aaaabab=1⟩φ(a) = a, φ(b) = b
107218⟨a, b | aaa=1, aaababa=1⟩φ(a) = a, φ(b) = b
107227⟨a, b | aaa=1, aababaa=1⟩φ(a) = a, φ(b) = b
107238⟨a, b | aaa=1, abaaaab=1⟩φ(a) = a, φ(b) = b
108054⟨a, b | aaa=1, abab=aaa⟩φ(a) = a, φ(b) = b
1110958⟨a, b | abab=aaa, baba=1⟩φ(a) = a, φ(b) = b
1116957⟨a, b | abab=1, aaaabab=1⟩φ(a) = a, φ(b) = b
1116962⟨a, b | abab=1, aaababa=1⟩φ(a) = a, φ(b) = b
1116971⟨a, b | abab=1, aababaa=1⟩φ(a) = a, φ(b) = b
1116981⟨a, b | abab=1, abaaaab=1⟩φ(a) = a, φ(b) = b
1116986⟨a, b | abab=1, ababaaa=1⟩φ(a) = a, φ(b) = b
1117001⟨a, b | abab=1, baaaaba=1⟩φ(a) = a, φ(b) = b
1117007⟨a, b | abab=1, babaaaa=1⟩φ(a) = a, φ(b) = b
1118008⟨a, b | abab=1, aaaaa=aa⟩φ(a) = a, φ(b) = b
1118013⟨a, b | abab=1, aaaab=ab⟩φ(a) = a, φ(b) = b
1118018⟨a, b | abab=1, aaaba=ba⟩φ(a) = a, φ(b) = b
1118037⟨a, b | abab=1, abaaa=ab⟩φ(a) = a, φ(b) = b
1118058⟨a, b | abab=1, baaaa=ba⟩φ(a) = a, φ(b) = b
1118071⟨a, b | abab=1, bbaaa=bb⟩φ(a) = a, φ(b) = b
1122211⟨a, b | aaa=1, aaabab=aa⟩φ(a) = a, φ(b) = b
1122227⟨a, b | aaa=1, aababa=aa⟩φ(a) = a, φ(b) = b
1122292⟨a, b | aaa=1, baaaab=aa⟩φ(a) = a, φ(b) = b
1122724⟨a, b | aaa=1, aaaaa=bab⟩φ(a) = a, φ(b) = b