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〈a, b | aaaa=a, bbbbb=a〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b20 ⇒ b5
  2. a ⇒ b5

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1bb2b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19
11bb2b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19
bbb2b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19b5
b2b2b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19b5b6
b3b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19b5b6b7
b4b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19b5b6b7b8
b5b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19b5b6b7b8b9
b6b6b7b8b9b10b11b12b13b14b15b16b17b18b19b5b6b7b8b9b10
b7b7b8b9b10b11b12b13b14b15b16b17b18b19b5b6b7b8b9b10b11
b8b8b9b10b11b12b13b14b15b16b17b18b19b5b6b7b8b9b10b11b12
b9b9b10b11b12b13b14b15b16b17b18b19b5b6b7b8b9b10b11b12b13
b10b10b11b12b13b14b15b16b17b18b19b5b6b7b8b9b10b11b12b13b14
b11b11b12b13b14b15b16b17b18b19b5b6b7b8b9b10b11b12b13b14b15
b12b12b13b14b15b16b17b18b19b5b6b7b8b9b10b11b12b13b14b15b16
b13b13b14b15b16b17b18b19b5b6b7b8b9b10b11b12b13b14b15b16b17
b14b14b15b16b17b18b19b5b6b7b8b9b10b11b12b13b14b15b16b17b18
b15b15b16b17b18b19b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19
b16b16b17b18b19b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19b5
b17b17b18b19b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19b5b6
b18b18b19b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19b5b6b7
b19b19b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19b5b6b7b8

Right 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=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