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〈a, b | aa=a, bbbbb=a〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. b10 ⇒ b5
  2. a ⇒ b5

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1bb2b3b4b5b6b7b8b9
11bb2b3b4b5b6b7b8b9
bbb2b3b4b5b6b7b8b9b5
b2b2b3b4b5b6b7b8b9b5b6
b3b3b4b5b6b7b8b9b5b6b7
b4b4b5b6b7b8b9b5b6b7b8
b5b5b6b7b8b9b5b6b7b8b9
b6b6b7b8b9b5b6b7b8b9b5
b7b7b8b9b5b6b7b8b9b5b6
b8b8b9b5b6b7b8b9b5b6b7
b9b9b5b6b7b8b9b5b6b7b8

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

37 unique, 902 total

Length:Presentation:Description:Related:
7 〈a, b | aa=1, abbb=b〉 Finite non-commutative monoid with 10 elements 51 isomorphic, 34 anti-isomorphic
8 〈a, b | aaa=b, abbb=1〉 Isomorphic to ℤ10 536 isomorphic
8 〈a, b | bb=aa, aba=a〉 Finite non-commutative monoid with 10 elements 1 isomorphic
8 〈a, b | bb=aa, aba=b〉 Finite non-commutative monoid with 10 elements 1 isomorphic
8 〈a, b | aa=a, bbb=ab〉 Finite non-commutative monoid with 10 elements 3 isomorphic
9 〈a, b | aab=bb, bba=a〉 Finite non-commutative monoid with 10 elements 6 isomorphic
9 〈a, b | aaa=b, abbb=a〉 Finite commutative monoid with 10 elements 59 isomorphic
9 〈a, b | aaa=b, abbb=b〉 Finite commutative monoid with 10 elements 35 isomorphic
9 〈a, b | bb=aa, aba=aa〉 Finite non-commutative monoid with 10 elements 1 isomorphic
9 〈a, b | aa=b, bbbbb=b〉 Finite commutative monoid with 10 elements 57 isomorphic
10 〈a, b | aaaa=b, aabb=b〉 Finite commutative monoid with 10 elements 20 isomorphic
10 〈a, b | aaa=bb, abb=ab〉 Finite non-commutative monoid with 10 elements 2 isomorphic
10 〈a, b | aaa=bb, abb=ba〉 Finite non-commutative monoid with 10 elements
10 〈a, b | aab=aa, aba=bb〉 Finite non-commutative monoid with 10 elements
10 〈a, b | aaa=b, abbb=bb〉 Finite commutative monoid with 10 elements 3 isomorphic
10 〈a, b | aab=a, baaa=bb〉 Finite non-commutative monoid with 10 elements
10 〈a, b | ab=aa, baaaa=b〉 Finite non-commutative monoid with 10 elements 14 isomorphic
10 〈a, b | ab=aa, baaa=bb〉 Finite non-commutative monoid with 10 elements 3 isomorphic
10 〈a, b | aa=a, abbbbb=b〉 Finite non-commutative monoid with 10 elements 5 isomorphic
10 〈a, b | ab=a, baaaa=bb〉 Finite non-commutative monoid with 10 elements 4 isomorphic
11 〈a, b | aaab=baa, abab=1〉 Finite non-Abelian group with 10 elements 3 isomorphic
11 〈a, b | aaaa=aa, abba=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aaaa=ab, baaa=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aaaa=bb, aaab=a〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aaaa=bb, aaab=b〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aabb=aa, bbbb=a〉 Finite commutative monoid with 10 elements 3 isomorphic
11 〈a, b | abab=aa, baab=b〉 Finite non-commutative monoid with 10 elements 4 isomorphic
11 〈a, b | aab=bb, aaaaa=b〉 Finite commutative monoid with 10 elements 7 isomorphic
11 〈a, b | aab=bb, abbbb=a〉 Finite commutative monoid with 10 elements 5 isomorphic
11 〈a, b | aba=aa, aaaab=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aab=b, abbbb=aa〉 Finite commutative monoid with 10 elements 5 isomorphic
11 〈a, b | aaa=b, abbb=bbb〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aab=a, bbbb=bab〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aab=b, aaaa=baa〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aba=b, aaaa=bbb〉 Finite commutative monoid with 10 elements
11 〈a, b | ab=a, bbbb=baaa〉 Finite non-commutative monoid with 10 elements
11 〈a, b | ab=a, bbbb=bbaa〉 Finite non-commutative monoid with 10 elements

Other isomorphic instances

17 total

Length:Presentation:
10〈a, b | aa=a, bbbbb=aa〉
11〈a, b | aabb=ab, bbbb=a〉
11〈a, b | aabb=ba, bbbb=a〉
11〈a, b | abab=ab, bbbb=a〉
11〈a, b | abab=ba, bbbb=a〉
11〈a, b | abba=ab, bbbb=a〉
11〈a, b | baab=ab, bbbb=a〉
11〈a, b | aab=a, bbbbb=ab〉
11〈a, b | aaa=b, abbb=aab〉
11〈a, b | aaa=b, abbb=aba〉
11〈a, b | aaa=b, abbb=baa〉
11〈a, b | aaa=b, babb=aab〉
11〈a, b | aaa=b, babb=aba〉
11〈a, b | aaa=b, babb=baa〉
11〈a, b | aa=a, bbbbb=aaa〉
11〈a, b | aa=b, bbbbb=abb〉
11〈a, b | aa=b, bbbbb=bab〉