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〈a, b | aaa=1, babab=aba〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b9 ⇒ b
  2. bab8 ⇒ ba
  3. b4a ⇒ ab4
  4. ba2b8 ⇒ ba2
  5. (ba)2 ⇒ abab7
  6. bab3a ⇒ ab3ab
  7. b2a2 ⇒ ab2ab6
  8. (b2a)2 ⇒ a2b6
  9. a3 ⇒ 1
  10. ba2ba ⇒ aba2b
  11. ba2b2a ⇒ a2b2ab7
  12. ba2b3a ⇒ abab2ab7

Idempotents

2 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

3 unique, 9 total

Length:Presentation:Description:Related:
9 〈a, b | bab=aaa, bbb=1〉 Finite non-commutative monoid with 147 elements 3 isomorphic
9 〈a, b | aaa=1, abbba=b〉 Finite non-commutative monoid with 147 elements 3 isomorphic
11 〈a, b | aaa=1, abababa=b〉 Finite non-commutative monoid with 147 elements