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〈a, b | aaab=bb, bbbb=a〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b13 ⇒ b2
  2. a ⇒ b4

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1bb2b3b4b5b6b7b8b9b10b11b12
11bb2b3b4b5b6b7b8b9b10b11b12
bbb2b3b4b5b6b7b8b9b10b11b12b2
b2b2b3b4b5b6b7b8b9b10b11b12b2b3
b3b3b4b5b6b7b8b9b10b11b12b2b3b4
b4b4b5b6b7b8b9b10b11b12b2b3b4b5
b5b5b6b7b8b9b10b11b12b2b3b4b5b6
b6b6b7b8b9b10b11b12b2b3b4b5b6b7
b7b7b8b9b10b11b12b2b3b4b5b6b7b8
b8b8b9b10b11b12b2b3b4b5b6b7b8b9
b9b9b10b11b12b2b3b4b5b6b7b8b9b10
b10b10b11b12b2b3b4b5b6b7b8b9b10b11
b11b11b12b2b3b4b5b6b7b8b9b10b11b12
b12b12b2b3b4b5b6b7b8b9b10b11b12b2

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

33 unique, 289 total

Length:Presentation:Description:Related:
9 〈a, b | aaaa=b, abbb=1〉 Isomorphic to ℤ13 189 isomorphic
9 〈a, b | aba=b, baab=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
10 〈a, b | aaaa=b, abbb=a〉 Finite commutative monoid with 13 elements 10 isomorphic
10 〈a, b | aaaa=b, abbb=b〉 Finite commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaab=b, abba=a〉 Finite non-commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aaa=ab, babb=b〉 Finite non-commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaa=ab, bba=bb〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=ab, bbb=ab〉 Finite non-commutative monoid with 13 elements 1 isomorphic
10 〈a, b | aaa=ab, bbb=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=bb, aab=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=b, abbbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aab=b, abbba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
10 〈a, b | bb=aa, aaab=ba〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=aa, bbbb=a〉 Finite commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=ab, bbbb=a〉 Finite commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaab=b, aabba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaba=b, babbb=a〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=bb, aabbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=ab, abbb=bb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, abbb=ba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, babb=ab〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=ab, bbbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbbb=aa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aba=bb, abbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ab, bbb=aaa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbb=aaa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbbbb=a〉 Finite commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=b, ababba=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=a, baaa=bbb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbb=bba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | ab=aa, aaaa=bbb〉 Finite non-commutative monoid with 13 elements 7 isomorphic
11 〈a, b | ab=aa, baaa=bbb〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | ab=a, baaaaaa=b〉 Finite non-commutative monoid with 13 elements

Other isomorphic instances

14 total

Length:Presentation:
11〈a, b | aaba=bb, bbbb=a〉
11〈a, b | aaa=bb, aabbb=a〉
11〈a, b | aaa=bb, ababb=a〉
11〈a, b | aaa=bb, abbab=a〉
11〈a, b | aaa=bb, abbba=a〉
11〈a, b | aaa=bb, baabb=a〉
11〈a, b | aaa=bb, babab=a〉
11〈a, b | aaa=b, abbbb=aa〉
11〈a, b | aaa=b, babbb=aa〉
11〈a, b | aaa=b, bbabb=aa〉
11〈a, b | aa=b, abbbbbb=b〉
11〈a, b | aa=b, babbbbb=b〉
11〈a, b | aa=b, bbabbbb=b〉
11〈a, b | aa=b, bbbabbb=b〉