Back

〈a, b | bab=aba, aaaa=1〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. bab ⇒ aba
  2. a4 ⇒ 1
  3. ba2ba ⇒ aba2b
  4. b4a ⇒ ab4
  5. b5 ⇒ b
  6. ba3ba ⇒ aba2b2
  7. ba2b3 ⇒ a3b2a
  8. b3a2b ⇒ ab2a3
  9. ba3b3 ⇒ a3b3a
  10. ba2b2a2 ⇒ a2b2a2b
  11. b2a2b2a ⇒ ab2a2b2
  12. b3a3b ⇒ ab3a3
  13. b2a3b2a ⇒ ab2a3b2
  14. ba3b2a3 ⇒ a3b2a3b
  15. ba3b2a2b ⇒ aba3b2a2

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 | 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
11 〈a, b | aaaa=1, abaaba=b〉 Finite non-commutative monoid with 100 elements