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〈a, b | ab=a, ba=b〉

Monoid presentation of length 6

Properties

Completion parameters

Complete rewriting system

  1. a2 ⇒ a
  2. ab ⇒ a
  3. ba ⇒ b
  4. b2 ⇒ b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1ab
11ab
aaaa
bbbb

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

5 unique, 2146 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 | aa=b, ab=b〉 Finite commutative monoid with 3 elements 23 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

61 total

Length:Presentation:
7〈a, b | ab=a, bab=b〉
7〈a, b | ab=a, bba=b〉
8〈a, b | ab=a, babb=b〉
8〈a, b | ab=a, bbab=b〉
8〈a, b | ab=a, bbba=b〉
9〈a, b | aab=a, baab=b〉
9〈a, b | aab=a, baba=b〉
9〈a, b | aab=a, babb=b〉
9〈a, b | aab=a, bbaa=b〉
9〈a, b | aab=a, bbab=b〉
9〈a, b | aab=a, bbba=b〉
9〈a, b | ab=a, babbb=b〉
9〈a, b | ab=a, bbabb=b〉
9〈a, b | ab=a, bbbab=b〉
9〈a, b | ab=a, bbbba=b〉
10〈a, b | ab=a, babbbb=b〉
10〈a, b | ab=a, bbabbb=b〉
10〈a, b | ab=a, bbbabb=b〉
10〈a, b | ab=a, bbbbab=b〉
10〈a, b | ab=a, bbbbba=b〉
11〈a, b | aaab=a, baaab=b〉
11〈a, b | aaab=a, baaba=b〉
11〈a, b | aaab=a, babaa=b〉
11〈a, b | aaab=a, bbaaa=b〉
11〈a, b | aaba=a, baaba=b〉
11〈a, b | aaba=a, babaa=b〉
11〈a, b | aaba=a, bbaaa=b〉
11〈a, b | aabb=a, babbb=b〉
11〈a, b | aabb=a, bbabb=b〉
11〈a, b | aabb=a, bbbab=b〉
11〈a, b | aabb=a, bbbba=b〉
11〈a, b | abab=a, babbb=b〉
11〈a, b | abab=a, bbabb=b〉
11〈a, b | abab=a, bbbab=b〉
11〈a, b | abab=a, bbbba=b〉
11〈a, b | aab=a, baaabb=b〉
11〈a, b | aab=a, baabab=b〉
11〈a, b | aab=a, baabba=b〉
11〈a, b | aab=a, baabbb=b〉
11〈a, b | aab=a, babaab=b〉
11〈a, b | aab=a, bababa=b〉
11〈a, b | aab=a, bababb=b〉
11〈a, b | aab=a, babbaa=b〉
11〈a, b | aab=a, babbab=b〉
11〈a, b | aab=a, babbba=b〉
11〈a, b | aab=a, bbaaab=b〉
11〈a, b | aab=a, bbaaba=b〉
11〈a, b | aab=a, bbaabb=b〉
11〈a, b | aab=a, bbabaa=b〉
11〈a, b | aab=a, bbabab=b〉
11〈a, b | aab=a, bbabba=b〉
11〈a, b | aab=a, bbbaaa=b〉
11〈a, b | aab=a, bbbaab=b〉
11〈a, b | aab=a, bbbaba=b〉
11〈a, b | aab=a, bbbbaa=b〉
11〈a, b | ab=a, babbbbb=b〉
11〈a, b | ab=a, bbabbbb=b〉
11〈a, b | ab=a, bbbabbb=b〉
11〈a, b | ab=a, bbbbabb=b〉
11〈a, b | ab=a, bbbbbab=b〉
11〈a, b | ab=a, bbbbbba=b〉