#17503 ⟨a, b | abab=1, aabbaa=b⟩

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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. a12 ⇒ 1
  2. a3b ⇒ ba3
  3. b2 ⇒ aba7
  4. bab ⇒ a11
  5. ba2b ⇒ a2ba2 
# ab:abab=1,aabbaa=b a/b
aaaaaaaaaaaa=1
aaab=baaa
bb=abaaaaaaa
bab=aaaaaaaaaaa
baab=aabaa

Right Cayley graph

Left Cayley graph

Others with same cardinality

4 unique, 18 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
1116966⟨a, b | abab=1, aaabbba=1⟩Finite non-Abelian group with 48 elements6 iso
1121751⟨a, b | aaa=1, abbbbbb=b⟩Finite non-commutative monoid with 48 elements1 iso