#18011 ⟨a, b | abab=1, aaaaa=bb⟩

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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. a35 ⇒ 1
  2. ab ⇒ ba29
  3. b2 ⇒ a5 
# ab:abab=1,aaaaa=bb a/b
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=1
ab=baaaaaaaaaaaaaaaaaaaaaaaaaaaaa
bb=aaaaa

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.

6 total

Σ#PresentationMapping
1126073⟨a, b | aa=1, ababbbbbb=1⟩φ(a) = ba, φ(b) = a
1126109⟨a, b | aa=1, abbbbbbab=1⟩φ(a) = ba, φ(b) = a
1126153⟨a, b | aa=1, bababbbbb=1⟩φ(a) = ba, φ(b) = a
1126174⟨a, b | aa=1, bbababbbb=1⟩φ(a) = ba, φ(b) = a
1126180⟨a, b | aa=1, bbbababbb=1⟩φ(a) = ba, φ(b) = a
1126690⟨a, b | aa=1, babbbbbb=a⟩φ(a) = ba, φ(b) = a