#10757 ⟨a, b | aaab=bba, abab=1⟩

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Quick links

  1. Properties
  2. Elements
  3. Right Cayley graph
  4. Left Cayley graph
  5. Rewriting system
  6. Isomorphic instances

Properties

Elements

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

Right Cayley graph

Left Cayley graph

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
#RuleProof
1. b9 ⇒ 1 [31]
2. b3a ⇒ ab6 [28]
3. aba ⇒ b8 [30]
4. ba2 ⇒ a2b4 [24]
5. bab2a ⇒ ab2ab7 [26]
6. a3 ⇒ b2ab8 [32]
7. a2b2a ⇒ bab2 [11]
# ab:aaab=bba,abab=1 b/a
bbbbbbbbb=1
bbba=abbbbbb
aba=bbbbbbbb
baa=aabbbb
babba=abbabbbbbbb
aaa=bbabbbbbbbb
aabba=babb

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