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〈a, b | aba=aaa, bbb=ab〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b7 ⇒ b6
  2. ab ⇒ b3
  3. b3a2 ⇒ b5a
  4. a3 ⇒ b3a

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2ba2b2ab3b2a2b3ab4b4ab5b5ab6b6a
11aba2bab2ba2b2ab3b2a2b3ab4b4ab5b5ab6b6a
aaa2b3b3ab3ab4b5ab4ab5b6ab5ab6b6ab6b6ab6b6a
bbbab2ba2b2ab3b2a2b3ab4b5ab4ab5b5ab6b6ab6b6a
a2a2b3ab5b5ab5ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
bababa2b4b4ab4ab5b6ab5ab6b6ab6ab6b6ab6b6ab6b6a
b2b2b2ab3b2a2b3ab4b5ab4ab5b6ab5ab6b6ab6b6ab6b6a
ba2ba2b4ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b2ab2ab2a2b5b5ab5ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b3b3b3ab4b5ab4ab5b6ab5ab6b6ab6ab6b6ab6b6ab6b6a
b2a2b2a2b5ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b3ab3ab5ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b4b4b4ab5b6ab5ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b4ab4ab6ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b5b5b5ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b5ab5ab6ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b6b6b6ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b6ab6ab6ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

19 unique, 71 total

Length:Presentation:Description:Related:
10 〈a, b | aaaa=b, abbbb=1〉 Isomorphic to ℤ17 39 isomorphic
10 〈a, b | aab=b, babbb=a〉 Finite non-commutative monoid with 17 elements 1 isomorphic
10 〈a, b | aba=b, baaab=a〉 Finite non-commutative monoid with 17 elements
10 〈a, b | aba=b, babbb=a〉 Finite non-commutative monoid with 17 elements
10 〈a, b | bb=aa, abab=aa〉 Finite non-commutative monoid with 17 elements
10 〈a, b | bb=aa, abab=ab〉 Finite non-commutative monoid with 17 elements
10 〈a, b | bb=aa, abab=ba〉 Finite non-commutative monoid with 17 elements
11 〈a, b | aab=aaa, bbb=ab〉 Finite non-commutative monoid with 17 elements
11 〈a, b | aab=aaa, bbb=ba〉 Finite non-commutative monoid with 17 elements
11 〈a, b | aba=aaa, baa=bb〉 Finite non-commutative monoid with 17 elements
11 〈a, b | abb=aba, bbb=aa〉 Finite non-commutative monoid with 17 elements
11 〈a, b | aaaa=b, abbbb=a〉 Finite commutative monoid with 17 elements 2 isomorphic
11 〈a, b | aaaa=b, abbbb=b〉 Finite commutative monoid with 17 elements 2 isomorphic
11 〈a, b | aabb=a, baaaa=b〉 Finite non-commutative monoid with 17 elements 1 isomorphic
11 〈a, b | abba=a, aaaab=b〉 Finite non-commutative monoid with 17 elements
11 〈a, b | aaa=ab, babbb=b〉 Finite non-commutative monoid with 17 elements 3 isomorphic
11 〈a, b | aab=aa, bbbb=ba〉 Finite non-commutative monoid with 17 elements
11 〈a, b | aab=bb, bab=aaa〉 Finite non-commutative monoid with 17 elements
11 〈a, b | aab=b, abbbba=a〉 Finite non-commutative monoid with 17 elements 4 isomorphic