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〈a, b | babb=aba, bbbb=1〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b4 ⇒ 1
  2. aba ⇒ bab2
  3. a2b2 ⇒ b2a2
  4. (ab2)2 ⇒ bab3a
  5. ab3ab2 ⇒ b(b2a)2
  6. a3 ⇒ a
  7. ab2a2 ⇒ ab2
  8. ab3a2 ⇒ b2ab3a

Idempotents

3 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

3 unique, 6 total

Length:Presentation:Description:Related:
10 〈a, b | aabb=ba, bbbb=1〉 Finite non-commutative monoid with 44 elements 1 isomorphic
10 〈a, b | baa=abb, aaaa=1〉 Finite non-commutative monoid with 44 elements 1 anti-isomorphic
11 〈a, b | abab=bba, bbbb=1〉 Finite non-commutative monoid with 44 elements 1 isomorphic

Other anti-isomorphic instances

1 total

Length:Presentation:
11〈a, b | aaaa=1, aabab=ba〉