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〈a, b | aab=aa, bbbb=ab〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b8 ⇒ b7
  2. ab ⇒ b4
  3. b7a ⇒ b7
  4. a2 ⇒ b7

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1abbab2b2ab3b3ab4b4ab5b5ab6b6ab7
11abbab2b2ab3b3ab4b4ab5b5ab6b6ab7
aab7b4b4ab5b5ab6b6ab7b7b7b7b7b7b7
bbbab2b2ab3b3ab4b4ab5b5ab6b6ab7b7b7
babab7b5b5ab6b6ab7b7b7b7b7b7b7b7b7
b2b2b2ab3b3ab4b4ab5b5ab6b6ab7b7b7b7b7
b2ab2ab7b6b6ab7b7b7b7b7b7b7b7b7b7b7
b3b3b3ab4b4ab5b5ab6b6ab7b7b7b7b7b7b7
b3ab3ab7b7b7b7b7b7b7b7b7b7b7b7b7b7
b4b4b4ab5b5ab6b6ab7b7b7b7b7b7b7b7b7
b4ab4ab7b7b7b7b7b7b7b7b7b7b7b7b7b7
b5b5b5ab6b6ab7b7b7b7b7b7b7b7b7b7b7
b5ab5ab7b7b7b7b7b7b7b7b7b7b7b7b7b7
b6b6b6ab7b7b7b7b7b7b7b7b7b7b7b7b7
b6ab6ab7b7b7b7b7b7b7b7b7b7b7b7b7b7
b7b7b7b7b7b7b7b7b7b7b7b7b7b7b7b7

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

23 unique, 190 total

Length:Presentation:Description:Related:
9 〈a, b | aaa=bb, aba=a〉 Finite non-commutative monoid with 15 elements 2 isomorphic
9 〈a, b | aaa=bb, aba=b〉 Finite non-commutative monoid with 15 elements 1 isomorphic
9 〈a, b | aaab=1, bbbbb=1〉 Isomorphic to ℤ15 138 isomorphic
9 〈a, b | aaa=a, abbb=b〉 Finite non-commutative monoid with 15 elements 4 isomorphic
10 〈a, b | aaa=bb, aba=aa〉 Finite non-commutative monoid with 15 elements 1 isomorphic
10 〈a, b | aaa=bb, aba=bb〉 Finite non-commutative monoid with 15 elements 2 isomorphic
10 〈a, b | aaa=a, bbbbb=a〉 Finite commutative monoid with 15 elements
10 〈a, b | aaa=b, bbbbb=a〉 Finite commutative monoid with 15 elements
10 〈a, b | aaa=b, bbbbb=b〉 Finite commutative monoid with 15 elements
11 〈a, b | abb=aaa, baaa=b〉 Finite non-commutative monoid with 15 elements 3 isomorphic
11 〈a, b | abb=aaa, baba=b〉 Finite non-commutative monoid with 15 elements 1 isomorphic
11 〈a, b | aab=aaa, aba=bb〉 Finite non-commutative monoid with 15 elements
11 〈a, b | abb=aaa, bbb=ab〉 Finite non-commutative monoid with 15 elements 1 isomorphic
11 〈a, b | abb=aaa, bbb=ba〉 Finite non-commutative monoid with 15 elements
11 〈a, b | aaa=aa, bbbbb=a〉 Finite commutative monoid with 15 elements
11 〈a, b | aaa=ab, baabb=b〉 Finite non-commutative monoid with 15 elements 5 isomorphic
11 〈a, b | aaa=ab, bbbbb=a〉 Finite commutative monoid with 15 elements 1 isomorphic
11 〈a, b | aaa=bb, bbbbb=a〉 Finite commutative monoid with 15 elements 1 isomorphic
11 〈a, b | aaa=ab, bbbb=aa〉 Finite non-commutative monoid with 15 elements
11 〈a, b | aaa=b, bbbbb=ab〉 Finite commutative monoid with 15 elements
11 〈a, b | aab=a, bbbbb=ba〉 Finite non-commutative monoid with 15 elements 1 anti-isomorphic
11 〈a, b | aab=b, bbaa=aaa〉 Finite non-commutative monoid with 15 elements
11 〈a, b | ab=aa, bbaaa=bb〉 Finite non-commutative monoid with 15 elements 6 isomorphic