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〈a, b | aaa=ab, baab=b〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a7 ⇒ a3
  2. ba4 ⇒ b
  3. ab ⇒ a3
  4. b2 ⇒ ba2

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3a5a6
11aba2baa3ba2a4ba3a5a6
aaa2a3a3a4a4a5a5a6a6a3
bbbaba2ba2ba3ba3bbbababa2
a2a2a3a4a4a5a5a6a6a3a3a4
bababa2ba3ba3bbbababa2ba2ba3
a3a3a4a5a5a6a6a3a3a4a4a5
ba2ba2ba3bbbababa2ba2ba3ba3b
a4a4a5a6a6a3a3a4a4a5a5a6
ba3ba3bbababa2ba2ba3ba3bbba
a5a5a6a3a3a4a4a5a5a6a6a3
a6a6a3a4a4a5a5a6a6a3a3a4

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

40 unique, 477 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=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, 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

3 total

Length:Presentation:
10〈a, b | aaa=ab, baba=b〉
10〈a, b | aaa=ab, bbaa=b〉
11〈a, b | aaa=ab, baaaa=b〉