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〈a, b | aaa=bb, abbb=ba〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b5 ⇒ b3
  2. ab4 ⇒ ab2
  3. ba ⇒ ab3
  4. a3 ⇒ b2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2abb2a2bab2b3a2b2ab3b4a2b3
11aba2abb2a2bab2b3a2b2ab3b4a2b3
aaa2abb2a2bab2b3a2b2ab3b4a2b3ab2b3
bbab3b2a2b3ab2b3a2b2ab3b4a2b3ab2b3a2b2
a2a2b2a2bab2b3a2b2ab3b4a2b3ab2b3a2b2ab3
ababa2b3ab2b3a2b2ab3b4a2b3ab2b3a2b2ab3b4
b2b2ab2b3a2b2ab3b4a2b3ab2b3a2b2ab3b4a2b3
a2ba2bb3a2b2ab3b4a2b3ab2b3a2b2ab3b4a2b3ab2
ab2ab2a2b2ab3b4a2b3ab2b3a2b2ab3b4a2b3ab2b3
b3b3ab3b4a2b3ab2b3a2b2ab3b4a2b3ab2b3a2b2
a2b2a2b2b4a2b3ab2b3a2b2ab3b4a2b3ab2b3a2b2ab3
ab3ab3a2b3ab2b3a2b2ab3b4a2b3ab2b3a2b2ab3b4
b4b4ab2b3a2b2ab3b4a2b3ab2b3a2b2ab3b4a2b3
a2b3a2b3b3a2b2ab3b4a2b3ab2b3a2b2ab3b4a2b3ab2

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=ab, abbb=bb〉 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