#7050 ⟨a, b | bb=aa, ababa=a⟩

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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. a10 ⇒ a2
  2. aba2 ⇒ ba7
  3. a2b ⇒ ba2
  4. b2 ⇒ a2
  5. a(ba)2 ⇒ a 
# ab:bb=aa,ababa=a a/b
aaaaaaaaaa=aa
abaa=baaaaaaa
aab=baa
bb=aa
ababa=a

Right Cayley graph

Left Cayley graph

Others with same cardinality

5 unique, 26 total

Σ#PresentationDescriptionRelated
93645⟨a, b | aa=1, abab=bbb⟩Finite non-commutative monoid with 26 elements12 iso, 7 anti-iso
105088⟨a, b | aaa=bb, baab=a⟩Finite non-commutative monoid with 26 elements1 iso
1115941⟨a, b | aba=bb, bbabb=a⟩Finite non-commutative monoid with 26 elements
1119766⟨a, b | aba=b, babbb=aa⟩Finite non-commutative monoid with 26 elements
1126639⟨a, b | aa=1, abbbbbbb=b⟩Finite non-commutative monoid with 26 elements1 iso