Back

〈a, b | aa=b, ab=b〉

Monoid presentation of length 6

Properties

Completion parameters

Complete rewriting system

  1. a3 ⇒ a2
  2. b ⇒ a2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aa2
11aa2
aaa2a2
a2a2a2a2

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

5 unique, 2184 total

Length:Presentation:Description:Related:
5 〈a, b | aa=b, ab=1〉 Isomorphic to ℤ3 2029 isomorphic
6 〈a, b | aa=b, ab=a〉 Finite commutative monoid with 3 elements 61 isomorphic
6 〈a, b | ab=a, ba=b〉 Finite non-commutative monoid with 3 elements 61 isomorphic
8 〈a, b | aa=a, abba=b〉 Finite commutative monoid with 3 elements 12 isomorphic
9 〈a, b | aba=a, aabb=b〉 Finite non-commutative monoid with 3 elements 16 isomorphic

Other isomorphic instances

23 total

Length:Presentation:
7〈a, b | aa=b, aaa=b〉
7〈a, b | aa=b, ab=aa〉
7〈a, b | ab=a, bb=ab〉
8〈a, b | aa=b, aaa=aa〉
8〈a, b | ab=a, abb=bb〉
9〈a, b | aab=aa, abb=b〉
9〈a, b | ab=a, abbb=bb〉
10〈a, b | aaa=aa, aaaa=b〉
10〈a, b | aab=aa, abbb=b〉
10〈a, b | ab=a, abbbb=bb〉
11〈a, b | aaab=aa, aabb=b〉
11〈a, b | aaab=aa, abab=b〉
11〈a, b | aaab=aa, abba=b〉
11〈a, b | aaab=aa, abbb=b〉
11〈a, b | aaba=aa, abba=b〉
11〈a, b | aaa=aa, aaaaa=b〉
11〈a, b | aab=aa, abbbb=b〉
11〈a, b | aab=a, aabbb=bb〉
11〈a, b | aab=a, ababb=bb〉
11〈a, b | aab=a, abbab=bb〉
11〈a, b | aab=a, abbba=bb〉
11〈a, b | aab=a, abbbb=bb〉
11〈a, b | ab=a, abbbbb=bb〉