#4118 ⟨a, b | bbb=aaa, abab=1⟩

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Properties

Elements

Elements in the center commute with all other elements.
The order of x is the least n such that xn = 1.

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. a24 ⇒ 1
  2. a3b ⇒ ba3
  3. b2 ⇒ aba4
  4. bab ⇒ a23
  5. ba2b ⇒ a2ba17 
# ab:bbb=aaa,abab=1 a/b
aaaaaaaaaaaaaaaaaaaaaaaa=1
aaab=baaa
bb=abaaaa
bab=aaaaaaaaaaaaaaaaaaaaaaa
baab=aabaaaaaaaaaaaaaaaaa

Right Cayley graph

Left Cayley graph

Other isomorphic instances

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

7 total

Σ#PresentationMapping
1126062⟨a, b | aa=1, abababbbb=1⟩φ(a) = ab, φ(b) = a
1126071⟨a, b | aa=1, ababbbbab=1⟩φ(a) = ab, φ(b) = a
1126105⟨a, b | aa=1, abbbbabab=1⟩φ(a) = ab, φ(b) = a
1126150⟨a, b | aa=1, babababbb=1⟩φ(a) = ab, φ(b) = a
1126173⟨a, b | aa=1, bbabababb=1⟩φ(a) = ab, φ(b) = a
1126680⟨a, b | aa=1, bababbbb=a⟩φ(a) = ab, φ(b) = a
1126688⟨a, b | aa=1, babbbbab=a⟩φ(a) = ab, φ(b) = a