Back

〈a, b | aaaa=aa, abbb=b〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b5 ⇒ b
  2. ab ⇒ b3
  3. a4 ⇒ a2

Idempotents

6 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
11aba2bab2a3ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
aaa2b3a3b3ab4a2b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3
bbbab2ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab4a3ba2ba3
a2a2a3ba2bab2a3ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
bababa2b4ba3b4abba2b4a2bab2b4a3ba2b2ab3ba3b2a2b3ab2a3b3a2b3a3
b2b2b2ab3b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3
a3a3a2b3a3b3ab4a2b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3
ba2ba2ba3b2ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab4a3ba2ba3
b2ab2ab2a2bb2a3bab2b2a2ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
b3b3b3ab4b3a2b4abb3a3b4a2bab2b4a3ba2b2ab3ba3b2a2b3ab2a3b3a2b3a3
ba3ba3ba2b4ba3b4abba2b4a2bab2b4a3ba2b2ab3ba3b2a2b3ab2a3b3a2b3a3
b2a2b2a2b2a3b3b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3
b3ab3ab3a2b2b3a3b2ab3b3a2b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab4a3ba2ba3
b4b4b4abb4a2bab2b4a3ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
b2a3b2a3b2a2bb2a3bab2b2a2ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
b3a2b3a2b3a3b4b3a2b4abb3a3b4a2bab2b4a3ba2b2ab3ba3b2a2b3ab2a3b3a2b3a3
b4ab4ab4a2b3b4a3b3ab4b4a2b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3
b3a3b3a3b3a2b2b3a3b2ab3b3a2b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab4a3ba2ba3
b4a2b4a2b4a3bb4a2bab2b4a3ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
b4a3b4a3b4a2b3b4a3b3ab4b4a2b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

28 unique, 65 total

Length:Presentation:Description:Related:
8 〈a, b | aab=a, bbbb=1〉 Finite non-commutative monoid with 20 elements 3 isomorphic, 1 anti-isomorphic
8 〈a, b | ab=aa, bbbb=1〉 Finite non-commutative monoid with 20 elements 1 isomorphic
9 〈a, b | abab=a, bbbb=1〉 Finite non-commutative monoid with 20 elements 2 isomorphic
9 〈a, b | aba=ab, bbbb=1〉 Finite non-commutative monoid with 20 elements 1 isomorphic, 1 anti-isomorphic
9 〈a, b | ab=aa, bbbb=b〉 Finite non-commutative monoid with 20 elements
10 〈a, b | abb=aab, aaaa=1〉 Finite non-commutative monoid with 20 elements 2 isomorphic
10 〈a, b | baa=abb, abab=1〉 Finite non-Abelian group with 20 elements 1 isomorphic, 1 anti-isomorphic
10 〈a, b | aaaaa=1, abbbb=1〉 Isomorphic to ℤ20 16 isomorphic
10 〈a, b | aab=bb, aaaa=a〉 Finite non-commutative monoid with 20 elements
10 〈a, b | aaa=bb, bab=aa〉 Finite non-commutative monoid with 20 elements 1 isomorphic
10 〈a, b | aba=a, aaaa=bb〉 Finite non-commutative monoid with 20 elements
10 〈a, b | aba=b, aaaa=bb〉 Finite non-commutative monoid with 20 elements
10 〈a, b | ab=aa, bbbb=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaab=bb, bbba=a〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaaa=a, bbbbb=a〉 Finite commutative monoid with 20 elements
11 〈a, b | aaaa=b, bbbbb=a〉 Finite commutative monoid with 20 elements
11 〈a, b | aaaa=b, bbbbb=b〉 Finite commutative monoid with 20 elements
11 〈a, b | aab=ba, abbabb=1〉 Finite non-Abelian group with 20 elements 2 isomorphic
11 〈a, b | aba=bb, baaab=a〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aab=aa, baba=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=aa, aaaa=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=aa, aaab=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=bb, abb=aaa〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaaa=1, aaabab=b〉 Finite non-commutative monoid with 20 elements 1 isomorphic
11 〈a, b | aaaa=1, aabab=ab〉 Finite non-commutative monoid with 20 elements 1 isomorphic
11 〈a, b | aba=b, aaaaabb=1〉 Finite non-Abelian group with 20 elements 3 isomorphic
11 〈a, b | aab=a, bbbbb=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | ab=aa, bbbb=bbb〉 Finite non-commutative monoid with 20 elements