#19706 ⟨a, b | aba=b, aaaaa=bb⟩

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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. a15 ⇒ a5
  2. ba10 ⇒ b
  3. ab ⇒ ba9
  4. b2 ⇒ a5 
# ab:aba=b,aaaaa=bb a/b
aaaaaaaaaaaaaaa=aaaaa
baaaaaaaaaa=b
ab=baaaaaaaaa
bb=aaaaa

Right Cayley graph

Left Cayley graph

Others with same cardinality

7 unique, 13 total

Σ#PresentationDescriptionRelated
104749⟨a, b | abba=b, baab=a⟩Finite non-commutative monoid with 25 elements
106381⟨a, b | aab=a, bbbbb=b⟩Finite non-commutative monoid with 25 elements1 iso
106536⟨a, b | aaa=a, aaba=bb⟩Finite non-commutative monoid with 25 elements
1111133⟨a, b | aaaaa=b, bbbbb=1⟩Isomorphic to ℤ253 iso
1114342⟨a, b | aaaa=a, aabba=b⟩Finite non-commutative monoid with 25 elements
1114869⟨a, b | abba=b, bbabb=a⟩Finite non-commutative monoid with 25 elements2 iso
1119634⟨a, b | aba=a, aaaaa=bb⟩Finite non-commutative monoid with 25 elements