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〈a, b | aab=ab, bbb=aaa〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b7 ⇒ b4
  2. ab ⇒ b4
  3. b3a ⇒ b6
  4. a3 ⇒ b3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2ba2b2ab3b2a2b4b5b6
11aba2bab2ba2b2ab3b2a2b4b5b6
aaa2b4b3b4b5b4b5b6b5b4b5b6
bbbab2ba2b2ab3b2a2b6b4b6b5b6b4
a2a2b3b4b6b4b5b4b5b6b5b4b5b6
bababa2b5b4b5b6b5b6b4b6b5b6b4
b2b2b2ab3b2a2b6b4b6b4b5b4b6b4b5
ba2ba2b4b5b4b5b6b5b6b4b6b5b6b4
b2ab2ab2a2b6b5b6b4b6b4b5b4b6b4b5
b3b3b6b4b6b4b5b4b5b6b5b4b5b6
b2a2b2a2b5b6b5b6b4b6b4b5b4b6b4b5
b4b4b4b5b4b5b6b5b6b4b6b5b6b4
b5b5b5b6b5b6b4b6b4b5b4b6b4b5
b6b6b6b4b6b4b5b4b5b6b5b4b5b6

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

33 unique, 302 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=ab, abbb=bb〉 Finite non-commutative monoid with 13 elements
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=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

Other isomorphic instances

1 total

Length:Presentation:
11〈a, b | aba=ab, bbb=aaa〉