#16966 ⟨a, b | abab=1, aaabbba=1⟩

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Properties

Element profile

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. a8 ⇒ 1
  2. a4b ⇒ ba4
  3. b2 ⇒ aba5
  4. bab ⇒ a7
  5. ba2b ⇒ a3ba7
  6. aba3b ⇒ (ba3)2 
# ab:abab=1,aaabbba=1 a/b
aaaaaaaa=1
aaaab=baaaa
bb=abaaaaa
bab=aaaaaaa
baab=aaabaaaaaaa
abaaab=baaabaaa

Right Cayley graph

Left Cayley graph

Others with same cardinality

4 unique, 12 total

Σ#PresentationDescriptionRelated
103771⟨a, b | aaaa=bb, abab=1⟩Finite non-Abelian group with 48 elements5 iso
1114993⟨a, b | aaa=bb, ababbb=1⟩Finite non-Abelian group with 48 elements2 iso
1117503⟨a, b | abab=1, aabbaa=b⟩Finite non-Abelian group with 48 elements
1121751⟨a, b | aaa=1, abbbbbb=b⟩Finite non-commutative monoid with 48 elements1 iso

Other isomorphic instances

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

6 total

Σ#PresentationMapping
1116977⟨a, b | abab=1, aabbbaa=1⟩φ(a) = a, φ(b) = b
1116979⟨a, b | abab=1, aabbbba=1⟩φ(a) = b, φ(b) = a
1116996⟨a, b | abab=1, abbbaaa=1⟩φ(a) = a, φ(b) = b
1116998⟨a, b | abab=1, abbbbaa=1⟩φ(a) = b, φ(b) = a
1117015⟨a, b | abab=1, bbbaaaa=1⟩φ(a) = a, φ(b) = b
1118069⟨a, b | abab=1, bbaaa=ab⟩φ(a) = a, φ(b) = b