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〈a, b | aaa=ab, bbb=ab〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a7 ⇒ a4
  2. ba3 ⇒ a5
  3. ab ⇒ a3
  4. b3 ⇒ a3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2aa4b2a2a5a6
11aba2bab2a3ba2b2aa4b2a2a5a6
aaa2a3a3a4a5a4a5a6a5a4a6a4
bbbab2ba2b2aa3a5b2a2a4a6a5a4a5
a2a2a3a4a4a5a6a5a6a4a6a5a4a5
bababa2a5a5a6a4a6a4a5a4a6a5a6
b2b2b2aa3b2a2a4a5a4a5a6a5a4a6a4
a3a3a4a5a5a6a4a6a4a5a4a6a5a6
ba2ba2a5a6a6a4a5a4a5a6a5a4a6a4
b2ab2ab2a2a4a4a5a6a5a6a4a6a5a4a5
a4a4a5a6a6a4a5a4a5a6a5a4a6a4
b2a2b2a2a4a5a5a6a4a6a4a5a4a6a5a6
a5a5a6a4a4a5a6a5a6a4a6a5a4a5
a6a6a4a5a5a6a4a6a4a5a4a6a5a6

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=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=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

Other isomorphic instances

1 total

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