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〈a, b | abb=aaa, bbb=ab〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b7 ⇒ b5
  2. ab ⇒ b3
  3. b4a ⇒ b6
  4. a3 ⇒ b4

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2ba2b2ab3b2a2b3ab4b3a2b5b6
11aba2bab2ba2b2ab3b2a2b3ab4b3a2b5b6
aaa2b3b4b3ab4b3a2b6b5b6b5b6b5b5b6
bbbab2ba2b2ab3b2a2b3ab4b3a2b6b5b6b6b5
a2a2b4b5b6b5b6b5b6b5b6b5b6b5b5b6
bababa2b4b5b6b5b6b5b6b5b6b5b6b6b5
b2b2b2ab3b2a2b3ab4b3a2b6b5b6b5b6b5b5b6
ba2ba2b5b6b5b6b5b6b5b6b5b6b5b6b6b5
b2ab2ab2a2b5b6b5b6b5b6b5b6b5b6b5b5b6
b3b3b3ab4b3a2b6b5b6b5b6b5b6b5b6b6b5
b2a2b2a2b6b5b6b5b6b5b6b5b6b5b6b5b5b6
b3ab3ab3a2b6b5b6b5b6b5b6b5b6b5b6b6b5
b4b4b6b5b6b5b6b5b6b5b6b5b6b5b5b6
b3a2b3a2b5b6b5b6b5b6b5b6b5b6b5b6b6b5
b5b5b5b6b5b6b5b6b5b6b5b6b5b6b6b5
b6b6b6b5b6b5b6b5b6b5b6b5b6b5b5b6

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

23 unique, 189 total

Length:Presentation:Description:Related:
9 〈a, b | aaa=bb, aba=a〉 Finite non-commutative monoid with 15 elements 2 isomorphic
9 〈a, b | aaa=bb, aba=b〉 Finite non-commutative monoid with 15 elements 1 isomorphic
9 〈a, b | aaab=1, bbbbb=1〉 Isomorphic to ℤ15 138 isomorphic
9 〈a, b | aaa=a, abbb=b〉 Finite non-commutative monoid with 15 elements 4 isomorphic
10 〈a, b | aaa=bb, aba=aa〉 Finite non-commutative monoid with 15 elements 1 isomorphic
10 〈a, b | aaa=bb, aba=bb〉 Finite non-commutative monoid with 15 elements 2 isomorphic
10 〈a, b | aaa=a, bbbbb=a〉 Finite commutative monoid with 15 elements
10 〈a, b | aaa=b, bbbbb=a〉 Finite commutative monoid with 15 elements
10 〈a, b | aaa=b, bbbbb=b〉 Finite commutative monoid with 15 elements
11 〈a, b | abb=aaa, baaa=b〉 Finite non-commutative monoid with 15 elements 3 isomorphic
11 〈a, b | abb=aaa, baba=b〉 Finite non-commutative monoid with 15 elements 1 isomorphic
11 〈a, b | aab=aaa, aba=bb〉 Finite non-commutative monoid with 15 elements
11 〈a, b | abb=aaa, bbb=ba〉 Finite non-commutative monoid with 15 elements
11 〈a, b | aaa=aa, bbbbb=a〉 Finite commutative monoid with 15 elements
11 〈a, b | aaa=ab, baabb=b〉 Finite non-commutative monoid with 15 elements 5 isomorphic
11 〈a, b | aaa=ab, bbbbb=a〉 Finite commutative monoid with 15 elements 1 isomorphic
11 〈a, b | aaa=bb, bbbbb=a〉 Finite commutative monoid with 15 elements 1 isomorphic
11 〈a, b | aaa=ab, bbbb=aa〉 Finite non-commutative monoid with 15 elements
11 〈a, b | aab=aa, bbbb=ab〉 Finite non-commutative monoid with 15 elements
11 〈a, b | aaa=b, bbbbb=ab〉 Finite commutative monoid with 15 elements
11 〈a, b | aab=a, bbbbb=ba〉 Finite non-commutative monoid with 15 elements 1 anti-isomorphic
11 〈a, b | aab=b, bbaa=aaa〉 Finite non-commutative monoid with 15 elements
11 〈a, b | ab=aa, bbaaa=bb〉 Finite non-commutative monoid with 15 elements 6 isomorphic

Other isomorphic instances

1 total

Length:Presentation:
11〈a, b | bab=aaa, bbb=ab〉