#19634 ⟨a, b | aba=a, 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. b9 ⇒ b2
  2. ab2 ⇒ b8
  3. b2a ⇒ b8
  4. aba ⇒ a
  5. a5 ⇒ b2 
# ab:aba=a,aaaaa=bb b/a
bbbbbbbbb=bb
abb=bbbbbbbb
bba=bbbbbbbb
aba=a
aaaaa=bb

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
1119706⟨a, b | aba=b, aaaaa=bb⟩Finite non-commutative monoid with 25 elements