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〈a, b | aaaa=ab, abbb=b〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a11 ⇒ a4
  2. b ⇒ a10

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aa2a3a4a5a6a7a8a9a10
11aa2a3a4a5a6a7a8a9a10
aaa2a3a4a5a6a7a8a9a10a4
a2a2a3a4a5a6a7a8a9a10a4a5
a3a3a4a5a6a7a8a9a10a4a5a6
a4a4a5a6a7a8a9a10a4a5a6a7
a5a5a6a7a8a9a10a4a5a6a7a8
a6a6a7a8a9a10a4a5a6a7a8a9
a7a7a8a9a10a4a5a6a7a8a9a10
a8a8a9a10a4a5a6a7a8a9a10a4
a9a9a10a4a5a6a7a8a9a10a4a5
a10a10a4a5a6a7a8a9a10a4a5a6

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

40 unique, 460 total

Length:Presentation:Description:Related:
9 〈a, b | aaa=bb, abbb=1〉 Isomorphic to ℤ11 259 isomorphic
10 〈a, b | abb=aaa, bba=b〉 Finite non-commutative monoid with 11 elements
10 〈a, b | aaa=ab, baab=b〉 Finite non-commutative monoid with 11 elements 3 isomorphic
10 〈a, b | aaa=bb, abbb=a〉 Finite commutative monoid with 11 elements 4 isomorphic
10 〈a, b | aaa=bb, abbb=b〉 Finite commutative monoid with 11 elements 3 isomorphic
10 〈a, b | aab=aa, baaa=b〉 Finite non-commutative monoid with 11 elements 4 isomorphic
10 〈a, b | aaa=ab, abb=bb〉 Finite non-commutative monoid with 11 elements 3 isomorphic
10 〈a, b | aaa=ab, bbb=aa〉 Finite non-commutative monoid with 11 elements 2 isomorphic
10 〈a, b | aab=bb, bab=aa〉 Finite non-commutative monoid with 11 elements 2 isomorphic
10 〈a, b | aaa=b, aabbb=a〉 Finite commutative monoid with 11 elements 35 isomorphic
10 〈a, b | aaa=b, aabbb=b〉 Finite commutative monoid with 11 elements 11 isomorphic
10 〈a, b | aab=a, bbbbb=a〉 Finite commutative monoid with 11 elements 1 isomorphic
10 〈a, b | aba=b, abb=aaa〉 Finite non-commutative monoid with 11 elements
10 〈a, b | ab=aa, bbbb=aa〉 Finite non-commutative monoid with 11 elements 1 isomorphic
10 〈a, b | ab=aa, bbbb=ba〉 Finite non-commutative monoid with 11 elements
10 〈a, b | aa=b, abbbbb=b〉 Finite commutative monoid with 11 elements 32 isomorphic
10 〈a, b | ab=a, baaaaa=b〉 Finite non-commutative monoid with 11 elements 6 isomorphic
10 〈a, b | ab=a, bbaaa=bb〉 Finite non-commutative monoid with 11 elements 4 isomorphic
11 〈a, b | aaab=aa, baaa=b〉 Finite non-commutative monoid with 11 elements 2 isomorphic
11 〈a, b | aaab=bb, abbb=a〉 Finite commutative monoid with 11 elements 6 isomorphic
11 〈a, b | aaab=a, babbb=b〉 Finite non-commutative monoid with 11 elements 4 isomorphic
11 〈a, b | aaba=a, abbbb=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aabb=a, baaab=b〉 Finite non-commutative monoid with 11 elements 7 isomorphic
11 〈a, b | abba=a, aaabb=b〉 Finite non-commutative monoid with 11 elements 2 isomorphic
11 〈a, b | aab=aa, bbbbb=a〉 Finite commutative monoid with 11 elements 1 isomorphic
11 〈a, b | aab=ab, bbbbb=a〉 Finite commutative monoid with 11 elements 8 isomorphic
11 〈a, b | aaa=bb, aaab=ab〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=ab, aaaa=bb〉 Finite non-commutative monoid with 11 elements 1 isomorphic
11 〈a, b | aab=ba, aaaa=bb〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aaa=a, aabbba=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=a, baaaaa=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=b, bbabbb=a〉 Finite commutative monoid with 11 elements 4 isomorphic
11 〈a, b | aba=a, aaaaab=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=b, abba=aaa〉 Finite non-commutative monoid with 11 elements 1 isomorphic
11 〈a, b | aab=b, baaa=aaa〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=b, bbbb=aaa〉 Finite commutative monoid with 11 elements
11 〈a, b | bb=aa, aaaaa=ab〉 Finite non-commutative monoid with 11 elements 7 isomorphic
11 〈a, b | bb=aa, aaaab=ab〉 Finite non-commutative monoid with 11 elements 7 isomorphic
11 〈a, b | ab=a, baaaa=bbb〉 Finite non-commutative monoid with 11 elements
11 〈a, b | ab=a, bbbaa=bbb〉 Finite non-commutative monoid with 11 elements

Other isomorphic instances

20 total

Length:Presentation:
11〈a, b | aaaa=b, aaabb=b〉
11〈a, b | aaaa=b, aabab=b〉
11〈a, b | aaaa=b, aabba=b〉
11〈a, b | aaaa=b, abaab=b〉
11〈a, b | aaaa=b, ababa=b〉
11〈a, b | aaaa=b, baaab=b〉
11〈a, b | aaa=b, aabbb=ab〉
11〈a, b | aaa=b, aabbb=ba〉
11〈a, b | aaa=b, ababb=ab〉
11〈a, b | aaa=b, ababb=ba〉
11〈a, b | aaa=b, abbab=ab〉
11〈a, b | aaa=b, abbab=ba〉
11〈a, b | aaa=b, abbba=ab〉
11〈a, b | aaa=b, baabb=ab〉
11〈a, b | aaa=b, baabb=ba〉
11〈a, b | aaa=b, babab=ab〉
11〈a, b | aab=a, bbbb=aaa〉
11〈a, b | aa=b, abbbbb=bb〉
11〈a, b | aa=b, babbbb=bb〉
11〈a, b | aa=b, bbabbb=bb〉