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〈a, b | ab=aa, bbbb=baa〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ a2
  2. b2a2 ⇒ ba3
  3. b4 ⇒ ba2
  4. a5 ⇒ a4

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2ab3a4ba3b3aba4
11aba2bab2a3ba2b2ab3a4ba3b3aba4
aaa2a2a3a3a3a4a4a4a4a4a4a4a4
bbbab2ba2b2ab3ba3ba3b3aba2ba4ba4ba3ba4
a2a2a3a3a4a4a4a4a4a4a4a4a4a4a4
bababa2ba2ba3ba3ba3ba4ba4ba4ba4ba4ba4ba4ba4
b2b2b2ab3ba3b3aba2ba4ba4ba3ba3ba4ba4ba4ba4
a3a3a4a4a4a4a4a4a4a4a4a4a4a4a4
ba2ba2ba3ba3ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4
b2ab2aba3ba3ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4
b3b3b3aba2ba4ba3ba3ba4ba4ba4ba4ba4ba4ba4ba4
a4a4a4a4a4a4a4a4a4a4a4a4a4a4a4
ba3ba3ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4
b3ab3aba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4
ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4

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=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=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, bbbb=bab〉