Back

〈a, b | aaaa=1, abaaba=b〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b7 ⇒ b
  2. bab6 ⇒ ba
  3. b3a ⇒ ab3
  4. ba2b6 ⇒ ba2
  5. (ba)2 ⇒ (ab)2
  6. bab2a ⇒ a2b2
  7. b2a2 ⇒ ab2ab
  8. ba3 ⇒ aba2b
  9. ba2ba ⇒ a3b
  10. ba2b2a ⇒ a2b2ab5
  11. a4 ⇒ 1

Idempotents

2 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

6 unique, 12 total

Length:Presentation:Description:Related:
9 〈a, b | baab=a, bbbb=1〉 Finite non-commutative monoid with 100 elements 2 isomorphic
9 〈a, b | aba=bb, aaaa=1〉 Finite non-commutative monoid with 100 elements 2 isomorphic
10 〈a, b | bab=aba, aaaa=1〉 Finite non-commutative monoid with 100 elements
10 〈a, b | aaaa=1, ababa=b〉 Finite non-commutative monoid with 100 elements
11 〈a, b | abba=bab, bbbb=1〉 Finite non-commutative monoid with 100 elements
11 〈a, b | aaaaa=1, ababbb=1〉 Finite non-Abelian group with 100 elements 2 isomorphic