Back

〈a, b | aaa=a, aabbba=b〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b5 ⇒ b
  2. ba ⇒ b3
  3. a2b ⇒ b
  4. a3 ⇒ a

Idempotents

4 elements

Cayley table

Idempotents are shown in bold.

1aba2abb2ab2b3ab3b4ab4
11aba2abb2ab2b3ab3b4ab4
aaa2ababab2b2ab3b3ab4b4
bbb3b2bb4b3bb4b2bb3
a2a2aba2abb2ab2b3ab3b4ab4
ababab3ab2abab4ab3abab4ab2abab3
b2b2b4b3b2bb4b2bb3b2b4
ab2ab2ab4ab3ab2abab4ab2abab3ab2ab4
b3b3bb4b3b2bb3b2b4b3b
ab3ab3abab4ab3ab2abab3ab2ab4ab3ab
b4b4b2bb4b3b2b4b3bb4b2
ab4ab4ab2abab4ab3ab2ab4ab3abab4ab2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

40 unique, 480 total

Length:Presentation:Description:Related:
9 〈a, b | aaa=bb, abbb=1〉 Isomorphic to ℤ11 259 isomorphic
10 〈a, b | abb=aaa, bba=b〉 Finite non-commutative monoid with 11 elements
10 〈a, b | aaa=ab, baab=b〉 Finite non-commutative monoid with 11 elements 3 isomorphic
10 〈a, b | aaa=bb, abbb=a〉 Finite commutative monoid with 11 elements 4 isomorphic
10 〈a, b | aaa=bb, abbb=b〉 Finite commutative monoid with 11 elements 3 isomorphic
10 〈a, b | aab=aa, baaa=b〉 Finite non-commutative monoid with 11 elements 4 isomorphic
10 〈a, b | aaa=ab, abb=bb〉 Finite non-commutative monoid with 11 elements 3 isomorphic
10 〈a, b | aaa=ab, bbb=aa〉 Finite non-commutative monoid with 11 elements 2 isomorphic
10 〈a, b | aab=bb, bab=aa〉 Finite non-commutative monoid with 11 elements 2 isomorphic
10 〈a, b | aaa=b, aabbb=a〉 Finite commutative monoid with 11 elements 35 isomorphic
10 〈a, b | aaa=b, aabbb=b〉 Finite commutative monoid with 11 elements 11 isomorphic
10 〈a, b | aab=a, bbbbb=a〉 Finite commutative monoid with 11 elements 1 isomorphic
10 〈a, b | aba=b, abb=aaa〉 Finite non-commutative monoid with 11 elements
10 〈a, b | ab=aa, bbbb=aa〉 Finite non-commutative monoid with 11 elements 1 isomorphic
10 〈a, b | ab=aa, bbbb=ba〉 Finite non-commutative monoid with 11 elements
10 〈a, b | aa=b, abbbbb=b〉 Finite commutative monoid with 11 elements 32 isomorphic
10 〈a, b | ab=a, baaaaa=b〉 Finite non-commutative monoid with 11 elements 6 isomorphic
10 〈a, b | ab=a, bbaaa=bb〉 Finite non-commutative monoid with 11 elements 4 isomorphic
11 〈a, b | aaaa=ab, abbb=b〉 Finite commutative monoid with 11 elements 20 isomorphic
11 〈a, b | aaab=aa, baaa=b〉 Finite non-commutative monoid with 11 elements 2 isomorphic
11 〈a, b | aaab=bb, abbb=a〉 Finite commutative monoid with 11 elements 6 isomorphic
11 〈a, b | aaab=a, babbb=b〉 Finite non-commutative monoid with 11 elements 4 isomorphic
11 〈a, b | aaba=a, abbbb=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aabb=a, baaab=b〉 Finite non-commutative monoid with 11 elements 7 isomorphic
11 〈a, b | abba=a, aaabb=b〉 Finite non-commutative monoid with 11 elements 2 isomorphic
11 〈a, b | aab=aa, bbbbb=a〉 Finite commutative monoid with 11 elements 1 isomorphic
11 〈a, b | aab=ab, bbbbb=a〉 Finite commutative monoid with 11 elements 8 isomorphic
11 〈a, b | aaa=bb, aaab=ab〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=ab, aaaa=bb〉 Finite non-commutative monoid with 11 elements 1 isomorphic
11 〈a, b | aab=ba, aaaa=bb〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=a, baaaaa=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=b, bbabbb=a〉 Finite commutative monoid with 11 elements 4 isomorphic
11 〈a, b | aba=a, aaaaab=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=b, abba=aaa〉 Finite non-commutative monoid with 11 elements 1 isomorphic
11 〈a, b | aab=b, baaa=aaa〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=b, bbbb=aaa〉 Finite commutative monoid with 11 elements
11 〈a, b | bb=aa, aaaaa=ab〉 Finite non-commutative monoid with 11 elements 7 isomorphic
11 〈a, b | bb=aa, aaaab=ab〉 Finite non-commutative monoid with 11 elements 7 isomorphic
11 〈a, b | ab=a, baaaa=bbb〉 Finite non-commutative monoid with 11 elements
11 〈a, b | ab=a, bbbaa=bbb〉 Finite non-commutative monoid with 11 elements