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〈a, b | aaa=bb, bab=aa〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a10 ⇒ a4
  2. ba8 ⇒ ba2
  3. aba2 ⇒ ba7
  4. a2b ⇒ ba4
  5. b2 ⇒ a3
  6. bab ⇒ a2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2abbaa3ababa2a4ba3a5ba4a6ba5a7ba6a8ba7a9
11aba2abbaa3ababa2a4ba3a5ba4a6ba5a7ba6a8ba7a9
aaa2aba3ba4abaa4ba5ba7a5ba2a6ba3a7ba4a8ba5a9ba6a4
bbbaa3ba2a2a4ba3a3a5ba4a6ba5a7ba6a8ba7a9ba2a4ba3
a2a2a3ba4a4ba3ba5a5ba4ba6a6ba7a7ba2a8ba3a9ba4a4ba5a5
abababaa4ba7a3a5ba2a4a6ba3a7ba4a8ba5a9ba6a4ba7a5ba2
bababa2a2ba3a7a3ba4a8a4ba5a5ba6a6ba7a7ba2a8ba3a9ba4
a3a3a4ba3a5ba2ba4a6ba3ba5a7ba6a8ba7a9ba2a4ba3a5ba4a6
abaababa7a3ba2a8a4ba3a9a5ba4a6ba5a7ba6a8ba7a9ba2a4ba3
ba2ba2ba3a7ba4a6a8ba5a7a9ba6a4ba7a5ba2a6ba3a7ba4a8ba5
a4a4a5ba2a6ba7ba3a7ba2ba4a8ba5a9ba6a4ba7a5ba2a6ba3a7
ba3ba3ba4a6ba5a5a7ba6a6a8ba7a9ba2a4ba3a5ba4a6ba5a7ba6
a5a5a6ba7a7ba6ba2a8ba7ba3a9ba4a4ba5a5ba6a6ba7a7ba2a8
ba4ba4ba5a5ba6a4a6ba7a5a7ba2a8ba3a9ba4a4ba5a5ba6a6ba7
a6a6a7ba6a8ba5ba7a9ba6ba2a4ba3a5ba4a6ba5a7ba6a8ba7a9
ba5ba5ba6a4ba7a9a5ba2a4a6ba3a7ba4a8ba5a9ba6a4ba7a5ba2
a7a7a8ba5a9ba4ba6a4ba5ba7a5ba2a6ba3a7ba4a8ba5a9ba6a4
ba6ba6ba7a9ba2a8a4ba3a9a5ba4a6ba5a7ba6a8ba7a9ba2a4ba3
a8a8a9ba4a4ba3ba5a5ba4ba6a6ba7a7ba2a8ba3a9ba4a4ba5a5
ba7ba7ba2a8ba3a7a9ba4a8a4ba5a5ba6a6ba7a7ba2a8ba3a9ba4
a9a9a4ba3a5ba2ba4a6ba3ba5a7ba6a8ba7a9ba2a4ba3a5ba4a6

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

28 unique, 64 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 | 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=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

Other isomorphic instances

1 total

Length:Presentation:
11〈a, b | aba=bb, abab=aa〉