#10757 ⟨a, b | aaab=bba, 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. b9 ⇒ 1
  2. b3a ⇒ ab6
  3. aba ⇒ b8
  4. ba2 ⇒ a2b4
  5. bab2a ⇒ ab2ab7
  6. a3 ⇒ b2ab8
  7. a2b2a ⇒ bab2 
# ab:aaab=bba,abab=1 b/a
bbbbbbbbb=1
bbba=abbbbbb
aba=bbbbbbbb
baa=aabbbb
babba=abbabbbbbbb
aaa=bbabbbbbbbb
aabba=babb

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.

5 total

Σ#PresentationMapping
1110762⟨a, b | aaab=bba, baba=1⟩φ(a) = a, φ(b) = b
1117493⟨a, b | abab=1, aaabba=b⟩φ(a) = a, φ(b) = b
1117520⟨a, b | abab=1, abbaaa=b⟩φ(a) = abb, φ(b) = bb
1118035⟨a, b | abab=1, aabba=bb⟩φ(a) = b, φ(b) = a
1118051⟨a, b | abab=1, abbaa=bb⟩φ(a) = bb, φ(b) = abb