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〈a, b | aabb=a, baabb=b〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a2 ⇒ a
  2. ba ⇒ b
  3. ab2 ⇒ a
  4. b3 ⇒ b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1ababb2
11ababb2
aaaababa
bbbb2b2b
abababaaab
b2b2b2bbb2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

16 unique, 1449 total

Length:Presentation:Description:Related:
6 〈a, b | aa=b, abb=1〉 Isomorphic to ℤ5 1132 isomorphic
7 〈a, b | aa=b, abb=a〉 Finite commutative monoid with 5 elements 71 isomorphic
7 〈a, b | aa=b, abb=b〉 Finite commutative monoid with 5 elements 43 isomorphic
7 〈a, b | ab=a, baa=b〉 Finite non-commutative monoid with 5 elements 43 isomorphic
8 〈a, b | aaa=b, aab=b〉 Finite commutative monoid with 5 elements 27 isomorphic
8 〈a, b | aab=a, baa=b〉 Finite non-commutative monoid with 5 elements 8 isomorphic
8 〈a, b | aab=b, aba=a〉 Finite non-commutative monoid with 5 elements 8 isomorphic
8 〈a, b | ab=a, bbbb=a〉 Finite commutative monoid with 5 elements 32 isomorphic
8 〈a, b | ab=a, aaa=bb〉 Finite commutative monoid with 5 elements 19 isomorphic
8 〈a, b | ab=a, bba=bb〉 Finite non-commutative monoid with 5 elements 15 isomorphic
8 〈a, b | ab=a, bbb=aa〉 Finite commutative monoid with 5 elements 9 isomorphic
8 〈a, b | ab=a, bbb=ba〉 Finite non-commutative monoid with 5 elements 4 isomorphic
9 〈a, b | aab=aa, bba=b〉 Finite non-commutative monoid with 5 elements 9 isomorphic
9 〈a, b | aab=b, aaba=a〉 Finite non-commutative monoid with 5 elements 10 isomorphic
10 〈a, b | aa=a, abbbba=b〉 Finite commutative monoid with 5 elements 3 isomorphic
11 〈a, b | aaa=aa, abbba=b〉 Finite commutative monoid with 5 elements

Other isomorphic instances

10 total

Length:Presentation:
11〈a, b | aabb=a, babba=b〉
11〈a, b | aabb=a, bbaab=b〉
11〈a, b | aabb=a, bbaba=b〉
11〈a, b | aabb=a, bbbaa=b〉
11〈a, b | abab=a, baabb=b〉
11〈a, b | abab=a, babab=b〉
11〈a, b | abab=a, babba=b〉
11〈a, b | abab=a, bbaab=b〉
11〈a, b | abab=a, bbaba=b〉
11〈a, b | abab=a, bbbaa=b〉

Other anti-isomorphic instances

3 total

Length:Presentation:
11〈a, b | abba=a, aabbb=b〉
11〈a, b | abba=a, ababb=b〉
11〈a, b | abba=a, abbab=b〉