#7249 ⟨a, b | aaa=1, ababbbb=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. b30 ⇒ 1
  2. b3a ⇒ ab3
  3. a2 ⇒ bab4
  4. aba ⇒ b26
  5. ab2a ⇒ b2ab20 
# ab:aaa=1,ababbbb=1 b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1
bbba=abbb
aa=babbbb
aba=bbbbbbbbbbbbbbbbbbbbbbbbbb
abba=bbabbbbbbbbbbbbbbbbbbbb

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.

12 total

Σ#PresentationMapping
107257⟨a, b | aaa=1, abbbbab=1⟩φ(a) = a, φ(b) = b
107270⟨a, b | aaa=1, bababbb=1⟩φ(a) = a, φ(b) = b
107276⟨a, b | aaa=1, bbababb=1⟩φ(a) = a, φ(b) = b
1114991⟨a, b | aaa=bb, ababab=1⟩φ(a) = babbbbbbbb, φ(b) = ab
1121194⟨a, b | aaa=1, abababbb=1⟩φ(a) = abbbbb, φ(b) = ab
1121198⟨a, b | aaa=1, ababbbab=1⟩φ(a) = abbbbb, φ(b) = ab
1121213⟨a, b | aaa=1, abbbabab=1⟩φ(a) = abbbbb, φ(b) = ab
1121238⟨a, b | aaa=1, babababb=1⟩φ(a) = abbbbb, φ(b) = ab
1121766⟨a, b | aaa=1, baabbbb=a⟩φ(a) = abbbbb, φ(b) = b
1121776⟨a, b | aaa=1, babbbab=a⟩φ(a) = abbbbb, φ(b) = b
1121784⟨a, b | aaa=1, bbababb=a⟩φ(a) = a, φ(b) = bb
1122314⟨a, b | aaa=1, babbbb=aa⟩φ(a) = a, φ(b) = b