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〈a, b | aaa=ab, bbb=aa〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a7 ⇒ a3
  2. ba2 ⇒ a4
  3. ab ⇒ a3
  4. b3 ⇒ a2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3b2aa4a5a6
11aba2bab2a3b2aa4a5a6
aaa2a3a3a4a5a4a6a5a6a3
bbbab2a4b2aa2a5a3a6a3a4
a2a2a3a4a4a5a6a5a3a6a3a4
babaa4a5a5a6a3a6a4a3a4a5
b2b2b2aa2a6a3a4a3a5a4a5a6
a3a3a4a5a5a6a3a6a4a3a4a5
b2ab2aa6a3a3a4a5a4a6a5a6a3
a4a4a5a6a6a3a4a3a5a4a5a6
a5a5a6a3a3a4a5a4a6a5a6a3
a6a6a3a4a4a5a6a5a3a6a3a4

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

40 unique, 478 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 | 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, 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

2 total

Length:Presentation:
11〈a, b | aaa=bb, aaab=ba〉
11〈a, b | aaa=bb, aaba=ba〉