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〈a, b | aa=a, bbbb=ab〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. b7 ⇒ b4
  2. ab ⇒ b4
  3. a2 ⇒ a

Idempotents

4 elements

Cayley table

Idempotents are shown in bold.

1abbab2b2ab3b3ab4b4ab5b5ab6b6a
11abbab2b2ab3b3ab4b4ab5b5ab6b6a
aaab4b4ab5b5ab6b6ab4b4ab5b5ab6b6a
bbbab2b2ab3b3ab4b4ab5b5ab6b6ab4b4a
bababab5b5ab6b6ab4b4ab5b5ab6b6ab4b4a
b2b2b2ab3b3ab4b4ab5b5ab6b6ab4b4ab5b5a
b2ab2ab2ab6b6ab4b4ab5b5ab6b6ab4b4ab5b5a
b3b3b3ab4b4ab5b5ab6b6ab4b4ab5b5ab6b6a
b3ab3ab3ab4b4ab5b5ab6b6ab4b4ab5b5ab6b6a
b4b4b4ab5b5ab6b6ab4b4ab5b5ab6b6ab4b4a
b4ab4ab4ab5b5ab6b6ab4b4ab5b5ab6b6ab4b4a
b5b5b5ab6b6ab4b4ab5b5ab6b6ab4b4ab5b5a
b5ab5ab5ab6b6ab4b4ab5b5ab6b6ab4b4ab5b5a
b6b6b6ab4b4ab5b5ab6b6ab4b4ab5b5ab6b6a
b6ab6ab6ab4b4ab5b5ab6b6ab4b4ab5b5ab6b6a

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

35 unique, 314 total

Length:Presentation:Description:Related:
8 〈a, b | aa=1, abbbb=b〉 Finite non-commutative monoid with 14 elements 14 isomorphic, 7 anti-isomorphic
9 〈a, b | aba=bb, bab=a〉 Finite non-commutative monoid with 14 elements 1 isomorphic
9 〈a, b | aa=1, ababbb=b〉 Finite non-commutative monoid with 14 elements 27 isomorphic, 10 anti-isomorphic
10 〈a, b | aaaa=bb, abbb=1〉 Isomorphic to ℤ14 165 isomorphic
10 〈a, b | aab=bb, bbba=a〉 Finite non-commutative monoid with 14 elements 5 isomorphic
10 〈a, b | aab=bb, aba=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
10 〈a, b | aab=b, bbba=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaaa=ab, baab=b〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | aaaa=bb, abbb=a〉 Finite commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aaaa=bb, abbb=b〉 Finite commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aabb=aa, baab=b〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | abab=aa, abba=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | abab=aa, baaa=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaaa=b, aabbb=a〉 Finite commutative monoid with 14 elements 15 isomorphic
11 〈a, b | aaaa=b, aabbb=b〉 Finite commutative monoid with 14 elements 5 isomorphic
11 〈a, b | aaa=bb, abbbb=b〉 Finite commutative monoid with 14 elements 11 isomorphic
11 〈a, b | aaa=bb, babbb=a〉 Finite commutative monoid with 14 elements
11 〈a, b | aab=aa, baaaa=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaa=ab, baab=bb〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aaa=bb, bbbb=ab〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aab=bb, abab=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aba=bb, bbbb=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aab=b, abbaa=aa〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | aab=b, babba=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aab=a, bbbb=baa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | ab=aa, bbbbb=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbbb=ba〉 Finite non-commutative monoid with 14 elements
11 〈a, b | ab=aa, bbaa=bbb〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbb=aaa〉 Finite non-commutative monoid with 14 elements 3 isomorphic
11 〈a, b | ab=aa, bbbb=baa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbb=bba〉 Finite non-commutative monoid with 14 elements
11 〈a, b | bb=aa, abab=aaa〉 Finite non-commutative monoid with 14 elements 2 anti-isomorphic
11 〈a, b | aa=a, bbbbbbb=a〉 Finite commutative monoid with 14 elements
11 〈a, b | aa=b, bbbbbbb=b〉 Finite commutative monoid with 14 elements
11 〈a, b | ab=a, bbaaaa=bb〉 Finite non-commutative monoid with 14 elements

Other isomorphic instances

2 total

Length:Presentation:
10〈a, b | aa=a, bbbb=aab〉
11〈a, b | aa=a, bbbb=aaab〉