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〈a, b | aba=aa, aaaa=bb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a9 ⇒ a5
  2. ba5 ⇒ a5
  3. aba ⇒ a2
  4. a4b ⇒ ba4
  5. b2 ⇒ a4

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2abbaa3a2bba2baba4a3bba3ba2ba5ba4ba3ba6a7a8
11aba2abbaa3a2bba2baba4a3bba3ba2ba5ba4ba3ba6a7a8
aaa2aba3a2ba2a4a3ba3a2ba5ba4a4a3ba6a5ba4a7a8a5
bbbaa4ba2baba5ba3ba2ba6a5ba4ba3ba7a6a5a8a7a6a7a8
a2a2a3a2ba4a3ba3a5ba4a4a3ba6a5a5ba4a7a6a5a8a5a6
ababa2a5a3a2ba6a4a3ba7a6a5ba4a8a7a6a5a8a7a8a5
bababa2babba3ba2bba2ba4ba3bba3ba2ba5a8ba4ba3ba6a5a8a7a8a5
a3a3a4a3ba5ba4a4a6a5a5ba4a7a6a6a5a8a7a6a5a6a7
a2ba2ba3a6a4a3ba7a5ba4a8a7a6a5a5a8a7a6a5a8a5a6
ba2ba2ba3ba2bba4ba3bba3a5a8ba4ba3ba6a5a5a8a7a6a5a8a5a6
babbabba2a5ba3ba2ba6ba4ba3ba7a6a5a8a8a7a6a5a8a7a8a5
a4a4a5ba4a6a5a5a7a6a6a5a8a7a7a6a5a8a7a6a7a8
a3ba3ba4a7a5ba4a8a6a5a5a8a7a6a6a5a8a7a6a5a6a7
ba3ba3ba4ba3ba5a8ba4a6a5a5a8a7a6a6a5a8a7a6a5a6a7
ba2bba2bba3a6ba4ba3ba7a5a8a8a7a6a5a5a8a7a6a5a8a5a6
a5a5a6a5a7a6a6a8a7a7a6a5a8a8a7a6a5a8a7a8a5
ba4ba4a5a8a6a5a5a7a6a6a5a8a7a7a6a5a8a7a6a7a8
ba3bba3bba4a7a5a8a8a6a5a5a8a7a6a6a5a8a7a6a5a6a7
a6a6a7a6a8a7a7a5a8a8a7a6a5a5a8a7a6a5a8a5a6
a7a7a8a7a5a8a8a6a5a5a8a7a6a6a5a8a7a6a5a6a7
a8a8a5a8a6a5a5a7a6a6a5a8a7a7a6a5a8a7a6a7a8

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, 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