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〈a, b | aaa=ab, abbb=bb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a8 ⇒ a5
  2. ba5 ⇒ a7
  3. ab ⇒ a3
  4. b2 ⇒ a7

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3a5ba4a6a7
11aba2baa3ba2a4ba3a5ba4a6a7
aaa2a3a3a4a4a5a5a6a6a7a7a5
bbbaa7ba2a5ba3a6ba4a7a7a5a5a6
a2a2a3a4a4a5a5a6a6a7a7a5a5a6
bababa2ba3ba3ba4ba4a7a7a5a5a6a6a7
a3a3a4a5a5a6a6a7a7a5a5a6a6a7
ba2ba2ba3ba4ba4a7a7a5a5a6a6a7a7a5
a4a4a5a6a6a7a7a5a5a6a6a7a7a5
ba3ba3ba4a7a7a5a5a6a6a7a7a5a5a6
a5a5a6a7a7a5a5a6a6a7a7a5a5a6
ba4ba4a7a5a5a6a6a7a7a5a5a6a6a7
a6a6a7a5a5a6a6a7a7a5a5a6a6a7
a7a7a5a6a6a7a7a5a5a6a6a7a7a5

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

33 unique, 303 total

Length:Presentation:Description:Related:
9 〈a, b | aaaa=b, abbb=1〉 Isomorphic to ℤ13 189 isomorphic
9 〈a, b | aba=b, baab=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
10 〈a, b | aaaa=b, abbb=a〉 Finite commutative monoid with 13 elements 10 isomorphic
10 〈a, b | aaaa=b, abbb=b〉 Finite commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaab=b, abba=a〉 Finite non-commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aaa=ab, babb=b〉 Finite non-commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaa=ab, bba=bb〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=ab, bbb=ab〉 Finite non-commutative monoid with 13 elements 1 isomorphic
10 〈a, b | aaa=ab, bbb=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=bb, aab=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=b, abbbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aab=b, abbba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
10 〈a, b | bb=aa, aaab=ba〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=aa, bbbb=a〉 Finite commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=ab, bbbb=a〉 Finite commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaab=bb, bbbb=a〉 Finite commutative monoid with 13 elements 14 isomorphic
11 〈a, b | aaab=b, aabba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaba=b, babbb=a〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=bb, aabbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=bb, abbb=ba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, babb=ab〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=ab, bbbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbbb=aa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aba=bb, abbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ab, bbb=aaa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbb=aaa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbbbb=a〉 Finite commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=b, ababba=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=a, baaa=bbb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbb=bba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | ab=aa, aaaa=bbb〉 Finite non-commutative monoid with 13 elements 7 isomorphic
11 〈a, b | ab=aa, baaa=bbb〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | ab=a, baaaaaa=b〉 Finite non-commutative monoid with 13 elements