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〈a, b | bab=aba, bbb=1〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. b3 ⇒ 1
  2. aba ⇒ bab
  3. a3b ⇒ ba3
  4. a4 ⇒ a
  5. ab2ab ⇒ bab2a
  6. ab2a2 ⇒ b2a2b
  7. a2b2a ⇒ ba2b2

Idempotents

2 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

14 unique, 90 total

Length:Presentation:Description:Related:
8 〈a, b | bab=aa, bbb=1〉 Finite non-commutative monoid with 27 elements 7 isomorphic
8 〈a, b | aaa=1, abba=b〉 Finite non-commutative monoid with 27 elements 7 isomorphic
8 〈a, b | aaa=1, babb=a〉 Finite non-Abelian group with 27 elements 21 isomorphic
9 〈a, b | bab=aa, bbb=b〉 Finite non-commutative monoid with 27 elements 1 isomorphic
9 〈a, b | aaa=1, aabbab=1〉 Finite non-Abelian group with 27 elements 23 isomorphic
9 〈a, b | aaa=1, ababa=b〉 Finite non-commutative monoid with 27 elements 3 isomorphic
10 〈a, b | aaa=aa, aba=bb〉 Finite non-commutative monoid with 27 elements
10 〈a, b | aaa=1, abaaba=b〉 Finite non-commutative monoid with 27 elements 1 isomorphic
10 〈a, b | aaa=1, baab=aba〉 Finite non-commutative monoid with 27 elements 1 isomorphic
11 〈a, b | aaba=b, aaabbb=1〉 Finite non-Abelian group with 27 elements 7 isomorphic
11 〈a, b | aaba=b, aabbab=1〉 Finite non-Abelian group with 27 elements 5 isomorphic
11 〈a, b | aaa=bb, aabaa=b〉 Finite non-commutative monoid with 27 elements
11 〈a, b | aaa=a, abbbbb=b〉 Finite non-commutative monoid with 27 elements
11 〈a, b | aba=b, bbbb=aaa〉 Finite non-commutative monoid with 27 elements

Other isomorphic instances

3 total

Length:Presentation:
10〈a, b | aaa=1, aabab=ba〉
11〈a, b | aaa=1, aababaa=b〉
11〈a, b | aaa=1, abab=aaba〉