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〈a, b | aaaa=1, abaab=ba〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b7 ⇒ b
  2. b6ab ⇒ ab
  3. ab2 ⇒ b4a
  4. b6a2b ⇒ a2b
  5. aba2 ⇒ b3ab
  6. a3b ⇒ b4(ba)3
  7. a(ab)2 ⇒ b5a2ba
  8. (ab)3 ⇒ b5a3
  9. a4 ⇒ 1

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 | abab=ba, bbbb=1〉 Finite non-commutative monoid with 64 elements
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 | aa=1, abababa=bb〉 Finite non-commutative monoid with 64 elements 2 isomorphic