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〈a, b | ab=aa, bbbbb=aa〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ a2
  2. ba2 ⇒ a3
  3. b5 ⇒ a2
  4. a6 ⇒ a3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3b2ab3a4b3ab4a5b4a
11aba2bab2a3b2ab3a4b3ab4a5b4a
aaa2a2a3a3a3a4a4a4a5a5a5a3a3
bbbab2a3b2ab3a4b3ab4a5b4aa2a3a3
a2a2a3a3a4a4a4a5a5a5a3a3a3a4a4
babaa3a3a4a4a4a5a5a5a3a3a3a4a4
b2b2b2ab3a4b3ab4a5b4aa2a3a3a3a4a4
a3a3a4a4a5a5a5a3a3a3a4a4a4a5a5
b2ab2aa4a4a5a5a5a3a3a3a4a4a4a5a5
b3b3b3ab4a5b4aa2a3a3a3a4a4a4a5a5
a4a4a5a5a3a3a3a4a4a4a5a5a5a3a3
b3ab3aa5a5a3a3a3a4a4a4a5a5a5a3a3
b4b4b4aa2a3a3a3a4a4a4a5a5a5a3a3
a5a5a3a3a4a4a4a5a5a5a3a3a3a4a4
b4ab4aa3a3a4a4a4a5a5a5a3a3a3a4a4

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

35 unique, 315 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=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=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

1 total

Length:Presentation:
11〈a, b | ab=aa, bbbbb=ab〉