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〈a, b | aab=b, abba=aaa〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b5 ⇒ b
  2. ab ⇒ b3
  3. ba2 ⇒ b3a
  4. a3 ⇒ b4a

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2b2ab3b3ab4b4a
11aba2bab2b2ab3b3ab4b4a
aaa2b3b4ab3ab4b4abbab2b2a
bbbab2b3ab2ab3b3ab4b4abba
a2a2b4abb2abab2b2ab3b3ab4b4a
babab3ab4bab4abbab2b2ab3b3a
b2b2b2ab3b4ab3ab4b4abbab2b2a
b2ab2ab4abb2abab2b2ab3b3ab4b4a
b3b3b3ab4bab4abbab2b2ab3b3a
b3ab3abab2b3ab2ab3b3ab4b4abba
b4b4b4abb2abab2b2ab3b3ab4b4a
b4ab4ab2ab3b4ab3ab4b4abbab2b2a

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

40 unique, 479 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 | aaaa=ab, abbb=b〉 Finite commutative monoid with 11 elements 20 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, 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

1 total

Length:Presentation:
11〈a, b | aab=b, baba=aaa〉