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〈a, b | aaa=ab, babb=bb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a8 ⇒ a5
  2. ab ⇒ a3
  3. b2 ⇒ ba5

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3a5ba4a6ba5a7ba6ba7
11aba2baa3ba2a4ba3a5ba4a6ba5a7ba6ba7
aaa2a3a3a4a4a5a5a6a6a7a7a5a5a6a7
bbbaba5ba2ba6ba3ba7ba4ba5ba5ba6ba6ba7ba7ba5ba6
a2a2a3a4a4a5a5a6a6a7a7a5a5a6a6a7a5
bababa2ba3ba3ba4ba4ba5ba5ba6ba6ba7ba7ba5ba5ba6ba7
a3a3a4a5a5a6a6a7a7a5a5a6a6a7a7a5a6
ba2ba2ba3ba4ba4ba5ba5ba6ba6ba7ba7ba5ba5ba6ba6ba7ba5
a4a4a5a6a6a7a7a5a5a6a6a7a7a5a5a6a7
ba3ba3ba4ba5ba5ba6ba6ba7ba7ba5ba5ba6ba6ba7ba7ba5ba6
a5a5a6a7a7a5a5a6a6a7a7a5a5a6a6a7a5
ba4ba4ba5ba6ba6ba7ba7ba5ba5ba6ba6ba7ba7ba5ba5ba6ba7
a6a6a7a5a5a6a6a7a7a5a5a6a6a7a7a5a6
ba5ba5ba6ba7ba7ba5ba5ba6ba6ba7ba7ba5ba5ba6ba6ba7ba5
a7a7a5a6a6a7a7a5a5a6a6a7a7a5a5a6a7
ba6ba6ba7ba5ba5ba6ba6ba7ba7ba5ba5ba6ba6ba7ba7ba5ba6
ba7ba7ba5ba6ba6ba7ba7ba5ba5ba6ba6ba7ba7ba5ba5ba6ba7

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

26 unique, 175 total

Length:Presentation:Description:Related:
8 〈a, b | bb=aa, abab=1〉 Finite non-Abelian group with 16 elements 4 isomorphic
8 〈a, b | aa=1, ababbb=1〉 Finite non-Abelian group with 16 elements 40 isomorphic
9 〈a, b | aaaa=b, bbbb=1〉 Isomorphic to ℤ16 67 isomorphic
9 〈a, b | aab=a, bbbb=b〉 Finite non-commutative monoid with 16 elements
10 〈a, b | aaab=ba, abab=1〉 Finite non-Abelian group with 16 elements 7 isomorphic
10 〈a, b | bab=aaa, aabb=1〉 Finite non-Abelian group with 16 elements 6 isomorphic
10 〈a, b | aaaa=a, aabb=b〉 Finite non-commutative monoid with 16 elements 1 isomorphic
10 〈a, b | aaaa=a, bbbb=a〉 Finite commutative monoid with 16 elements 1 isomorphic
10 〈a, b | aaaa=b, bbbb=a〉 Finite commutative monoid with 16 elements 5 isomorphic
10 〈a, b | aba=b, aaaabb=1〉 Finite non-Abelian group with 16 elements 3 isomorphic
10 〈a, b | aba=b, aabbbb=1〉 Finite non-Abelian group with 16 elements 5 isomorphic
11 〈a, b | aaaa=aa, bbbb=a〉 Finite commutative monoid with 16 elements
11 〈a, b | aaaa=ab, bbbb=a〉 Finite commutative monoid with 16 elements 2 isomorphic
11 〈a, b | aaaa=bb, bbbb=a〉 Finite commutative monoid with 16 elements
11 〈a, b | aaab=bb, abba=a〉 Finite non-commutative monoid with 16 elements 2 isomorphic
11 〈a, b | bab=aab, bbb=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | bab=aba, bbb=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaaa=a, aabab=b〉 Finite non-commutative monoid with 16 elements 1 isomorphic
11 〈a, b | aab=bb, abbba=a〉 Finite non-commutative monoid with 16 elements 3 isomorphic
11 〈a, b | aaa=ab, bbaa=bb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=bb, abab=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aba=aa, bbbb=ab〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=b, abbbbb=b〉 Finite commutative monoid with 16 elements 2 isomorphic
11 〈a, b | aba=b, aaaa=abb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | ab=aa, bbba=bbb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aa=a, ababab=bb〉 Finite non-commutative monoid with 16 elements