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〈a, b | aba=b, aaaa=bb〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a12 ⇒ a4
  2. ba8 ⇒ b
  3. ab ⇒ ba7
  4. b2 ⇒ a4

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3a5ba4a6ba5a7ba6a8ba7a9a10a11
11aba2baa3ba2a4ba3a5ba4a6ba5a7ba6a8ba7a9a10a11
aaa2ba7a3ba4baa5ba2a6ba3a7ba4a8ba5a9ba6a10a11a4
bbbaa4ba2a5ba3a6ba4a7ba5a8ba6a9ba7a10ba11baba2ba3
a2a2a3ba6a4ba7a5ba6baa7ba2a8ba3a9ba4a10ba5a11a4a5
bababa2a11ba3a4ba4a5ba5a6ba6a7ba7a8ba9baa10ba2ba3ba4
a3a3a4ba5a5ba6a6ba7a7ba8baa9ba2a10ba3a11ba4a4a5a6
ba2ba2ba3a10ba4a11ba5a4ba6a5ba7a6ba7baa8ba2a9ba3ba4ba5
a4a4a5ba4a6ba5a7ba6a8ba7a9ba10baa11ba2a4ba3a5a6a7
ba3ba3ba4a9ba5a10ba6a11ba7a4ba5baa6ba2a7ba3a8ba4ba5ba6
a5a5a6ba3a7ba4a8ba5a9ba6a10ba7a11ba4baa5ba2a6a7a8
ba4ba4ba5a8ba6a9ba7a10ba11baa4ba2a5ba3a6ba4a7ba5ba6ba7
a6a6a7ba2a8ba3a9ba4a10ba5a11ba6a4ba7a5ba6baa7a8a9
ba5ba5ba6a7ba7a8ba9baa10ba2a11ba3a4ba4a5ba5a6ba6ba7b
a7a7a8baa9ba2a10ba3a11ba4a4ba5a5ba6a6ba7a7ba8a9a10
ba6ba6ba7a6ba7baa8ba2a9ba3a10ba4a11ba5a4ba6a5ba7bba
a8a8a9ba10baa11ba2a4ba3a5ba4a6ba5a7ba6a8ba7a9a10a11
ba7ba7ba5baa6ba2a7ba3a8ba4a9ba5a10ba6a11ba7a4bbaba2
a9a9a10ba7a11ba4baa5ba2a6ba3a7ba4a8ba5a9ba6a10a11a4
a10a10a11ba6a4ba7a5ba6baa7ba2a8ba3a9ba4a10ba5a11a4a5
a11a11a4ba5a5ba6a6ba7a7ba8baa9ba2a10ba3a11ba4a4a5a6

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 | 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=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