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〈a, b | abab=ba, bbbb=1〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. b4 ⇒ 1
  2. aba ⇒ bab3
  3. a2b ⇒ b(b2a)2
  4. ab3ab2 ⇒ b2ab3a
  5. ab2ab3 ⇒ ba2
  6. ab2a2 ⇒ b2ab2
  7. (ab2)3 ⇒ b2a3
  8. ab3a3 ⇒ b3ab
  9. a5 ⇒ a

Idempotents

2 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

6 unique, 15 total

Length:Presentation:Description:Related:
9 〈a, b | aab=ba, bbbb=1〉 Finite non-commutative monoid with 64 elements 2 isomorphic
10 〈a, b | aaaa=1, ababbb=1〉 Finite non-Abelian group with 64 elements 2 isomorphic
10 〈a, b | aa=1, ababa=bbb〉 Finite non-commutative monoid with 64 elements 2 isomorphic
11 〈a, b | baab=abb, bbbb=1〉 Finite non-commutative monoid with 64 elements 1 isomorphic
11 〈a, b | aaaa=1, abaab=ba〉 Finite non-commutative monoid with 64 elements
11 〈a, b | aa=1, abababa=bb〉 Finite non-commutative monoid with 64 elements 2 isomorphic