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〈a, b | aba=aa, aaab=bb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a8 ⇒ a5
  2. ba4 ⇒ a7
  3. aba ⇒ a2
  4. a7b ⇒ a4b
  5. b2 ⇒ a3b
  6. ba3b ⇒ a6b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2abbaa3a2bba2baba4a3bba3ba2ba5a4ba6a5ba7a6b
11aba2abbaa3a2bba2baba4a3bba3ba2ba5a4ba6a5ba7a6b
aaa2aba3a2ba2a4a3ba3a2ba5a4ba4a3ba6a5ba7a6ba5a4b
bbbaa3bba2baba4ba3ba2ba5a4ba7a6ba6a5ba5a4ba6a5ba7a6b
a2a2a3a2ba4a3ba3a5a4ba4a3ba6a5ba5a4ba7a6ba5a4ba6a5b
ababa2a4ba3a2ba5a4a3ba6a5ba5a4ba7a6ba6a5ba7a6ba5a4b
bababa2babba3ba2bba2a7a6bba3ba2ba5a4ba7a6ba6a5ba7a6ba5a4b
a3a3a4a3ba5a4ba4a6a5ba5a4ba7a6ba6a5ba5a4ba6a5ba7a6b
a2ba2ba3a5ba4a3ba6a5a4ba7a6ba6a5ba5a4ba7a6ba5a4ba6a5b
ba2ba2ba3ba2ba7a6bba3a5a4ba7a6ba6a5ba5a4ba7a6ba5a4ba6a5b
babbabba2a4bba3ba2ba5a7a6ba6a5ba5a4ba7a6ba6a5ba7a6ba5a4b
a4a4a5a4ba6a5ba5a7a6ba6a5ba5a4ba7a6ba6a5ba7a6ba5a4b
a3ba3ba4a6ba5a4ba7a6a5ba5a4ba7a6ba6a5ba5a4ba6a5ba7a6b
ba3ba3a7a6ba5a4ba7a6a5ba5a4ba7a6ba6a5ba5a4ba6a5ba7a6b
ba2bba2bba3a5ba7a6ba6a5a4ba7a6ba6a5ba5a4ba7a6ba5a4ba6a5b
a5a5a6a5ba7a6ba6a5a4ba7a6ba6a5ba5a4ba7a6ba5a4ba6a5b
a4ba4ba5a4ba6a5ba5a7a6ba6a5ba5a4ba7a6ba6a5ba7a6ba5a4b
a6a6a7a6ba5a4ba7a6a5ba5a4ba7a6ba6a5ba5a4ba6a5ba7a6b
a5ba5ba6a5ba7a6ba6a5a4ba7a6ba6a5ba5a4ba7a6ba5a4ba6a5b
a7a7a5a4ba6a5ba5a7a6ba6a5ba5a4ba7a6ba6a5ba7a6ba5a4b
a6ba6ba7a6ba5a4ba7a6a5ba5a4ba7a6ba6a5ba5a4ba6a5ba7a6b

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 | aaaa=aa, abbb=b〉 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=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