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〈a, b | ab=aa, aaaa=bbb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ a2
  2. a4 ⇒ b3
  3. b3a ⇒ b3
  4. b4 ⇒ b3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2ab3ba3b2a2b2a3
11aba2bab2a3ba2b2ab3ba3b2a2b2a3
aaa2a2a3a3a3b3b3b3b3b3b3b3
bbbab2ba2b2ab3ba3b2a2b3b3b2a3b3b3
a2a2a3a3b3b3b3b3b3b3b3b3b3b3
bababa2ba2ba3ba3ba3b3b3b3b3b3b3b3
b2b2b2ab3b2a2b3b3b2a3b3b3b3b3b3b3
a3a3b3b3b3b3b3b3b3b3b3b3b3b3
ba2ba2ba3ba3b3b3b3b3b3b3b3b3b3b3
b2ab2ab2a2b2a2b2a3b2a3b2a3b3b3b3b3b3b3b3
b3b3b3b3b3b3b3b3b3b3b3b3b3b3
ba3ba3b3b3b3b3b3b3b3b3b3b3b3b3
b2a2b2a2b2a3b2a3b3b3b3b3b3b3b3b3b3b3
b2a3b2a3b3b3b3b3b3b3b3b3b3b3b3b3

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

33 unique, 296 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=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, 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

7 total

Length:Presentation:
11〈a, b | ab=aa, aaab=bbb〉
11〈a, b | ab=aa, aaba=bbb〉
11〈a, b | ab=aa, aabb=bbb〉
11〈a, b | ab=aa, abaa=bbb〉
11〈a, b | ab=aa, abab=bbb〉
11〈a, b | ab=aa, abba=bbb〉
11〈a, b | ab=aa, abbb=bbb〉