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〈a, b | aaaa=b, aabbb=a〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a14 ⇒ a
  2. b ⇒ a4

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aa2a3a4a5a6a7a8a9a10a11a12a13
11aa2a3a4a5a6a7a8a9a10a11a12a13
aaa2a3a4a5a6a7a8a9a10a11a12a13a
a2a2a3a4a5a6a7a8a9a10a11a12a13aa2
a3a3a4a5a6a7a8a9a10a11a12a13aa2a3
a4a4a5a6a7a8a9a10a11a12a13aa2a3a4
a5a5a6a7a8a9a10a11a12a13aa2a3a4a5
a6a6a7a8a9a10a11a12a13aa2a3a4a5a6
a7a7a8a9a10a11a12a13aa2a3a4a5a6a7
a8a8a9a10a11a12a13aa2a3a4a5a6a7a8
a9a9a10a11a12a13aa2a3a4a5a6a7a8a9
a10a10a11a12a13aa2a3a4a5a6a7a8a9a10
a11a11a12a13aa2a3a4a5a6a7a8a9a10a11
a12a12a13aa2a3a4a5a6a7a8a9a10a11a12
a13a13aa2a3a4a5a6a7a8a9a10a11a12a13

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

35 unique, 301 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=a, bbbb=ab〉 Finite non-commutative monoid with 14 elements 2 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=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

15 total

Length:Presentation:
11〈a, b | aaaa=b, ababb=a〉
11〈a, b | aaaa=b, abbab=a〉
11〈a, b | aaaa=b, abbba=a〉
11〈a, b | aaaa=b, baabb=a〉
11〈a, b | aaaa=b, babab=a〉
11〈a, b | aaa=b, aabbbb=a〉
11〈a, b | aaa=b, ababbb=a〉
11〈a, b | aaa=b, abbabb=a〉
11〈a, b | aaa=b, abbbab=a〉
11〈a, b | aaa=b, abbbba=a〉
11〈a, b | aaa=b, baabbb=a〉
11〈a, b | aaa=b, bababb=a〉
11〈a, b | aaa=b, babbab=a〉
11〈a, b | aaa=b, bbaabb=a〉
11〈a, b | aa=b, bbbbbbb=a〉