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〈a, b | abb=aaa, aaab=b〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b7 ⇒ b
  2. ab ⇒ b5
  3. ba ⇒ b5
  4. a3 ⇒ b6

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2b2b3b4b5b6
11aba2b2b3b4b5b6
aaa2b5b6b6bb2b3b4
bbb5b2b3b3b4b5b6b
a2a2b6b3b4b4b5b6bb2
b2b2b6b3b4b4b5b6bb2
b3b3bb4b5b5b6bb2b3
b4b4b2b5b6b6bb2b3b4
b5b5b3b6bbb2b3b4b5
b6b6b4bb2b2b3b4b5b6

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

38 unique, 935 total

Length:Presentation:Description:Related:
7 〈a, b | aaa=b, bbb=1〉 Isomorphic to ℤ9 562 isomorphic
8 〈a, b | aaa=a, abb=b〉 Finite non-commutative monoid with 9 elements 2 isomorphic
8 〈a, b | aaa=a, bbb=a〉 Finite commutative monoid with 9 elements 48 isomorphic
8 〈a, b | aaa=b, bbb=a〉 Finite commutative monoid with 9 elements 62 isomorphic
8 〈a, b | aba=b, bab=a〉 Finite non-commutative monoid with 9 elements 3 isomorphic
9 〈a, b | aaa=aa, bbb=a〉 Finite commutative monoid with 9 elements 16 isomorphic
9 〈a, b | aaa=ab, bab=b〉 Finite non-commutative monoid with 9 elements 4 isomorphic
9 〈a, b | aaa=ab, bbb=a〉 Finite commutative monoid with 9 elements 40 isomorphic
9 〈a, b | aaa=bb, bbb=a〉 Finite commutative monoid with 9 elements 70 isomorphic
9 〈a, b | aaa=a, abab=b〉 Finite non-commutative monoid with 9 elements 2 isomorphic
9 〈a, b | aaa=a, abba=b〉 Finite non-commutative monoid with 9 elements 2 isomorphic
9 〈a, b | aab=b, abba=a〉 Finite non-commutative monoid with 9 elements 13 isomorphic
9 〈a, b | ab=aa, bba=bb〉 Finite non-commutative monoid with 9 elements
9 〈a, b | ab=a, baaaa=b〉 Finite non-commutative monoid with 9 elements 20 isomorphic
10 〈a, b | aab=aaa, baa=b〉 Finite non-commutative monoid with 9 elements 1 isomorphic
10 〈a, b | aab=aaa, bbb=a〉 Finite commutative monoid with 9 elements 1 isomorphic
10 〈a, b | abb=aaa, bbb=a〉 Finite commutative monoid with 9 elements 12 isomorphic
10 〈a, b | aaa=aa, abbb=b〉 Finite non-commutative monoid with 9 elements 3 isomorphic
10 〈a, b | aaa=bb, aaba=b〉 Finite commutative monoid with 9 elements
10 〈a, b | aab=aa, bbbb=a〉 Finite commutative monoid with 9 elements 5 isomorphic
10 〈a, b | aaa=bb, aab=ab〉 Finite non-commutative monoid with 9 elements 1 isomorphic
10 〈a, b | aaa=a, ababa=b〉 Finite non-commutative monoid with 9 elements
10 〈a, b | aab=a, baaaa=b〉 Finite non-commutative monoid with 9 elements
10 〈a, b | aba=a, aaaab=b〉 Finite non-commutative monoid with 9 elements
10 〈a, b | aab=b, bbb=aaa〉 Finite commutative monoid with 9 elements 1 isomorphic
10 〈a, b | bb=aa, aaaa=ab〉 Finite non-commutative monoid with 9 elements 2 isomorphic
10 〈a, b | bb=aa, aabb=ba〉 Finite non-commutative monoid with 9 elements
10 〈a, b | ab=a, baaa=bbb〉 Finite non-commutative monoid with 9 elements 3 isomorphic
10 〈a, b | ab=a, bbaa=bbb〉 Finite non-commutative monoid with 9 elements 2 isomorphic
11 〈a, b | aba=aaa, aaab=b〉 Finite non-commutative monoid with 9 elements 3 isomorphic
11 〈a, b | aaab=a, baaaa=b〉 Finite non-commutative monoid with 9 elements 1 isomorphic
11 〈a, b | aab=b, aaaaa=ba〉 Finite non-commutative monoid with 9 elements
11 〈a, b | aab=b, aaaaa=bb〉 Finite commutative monoid with 9 elements
11 〈a, b | aab=b, abaa=aaa〉 Finite non-commutative monoid with 9 elements
11 〈a, b | aab=b, babb=aaa〉 Finite commutative monoid with 9 elements 3 isomorphic
11 〈a, b | aba=a, abab=bbb〉 Finite non-commutative monoid with 9 elements
11 〈a, b | ab=aa, aaaaa=bb〉 Finite non-commutative monoid with 9 elements 15 isomorphic
11 〈a, b | ab=a, bbbbb=baa〉 Finite non-commutative monoid with 9 elements

Other isomorphic instances

7 total

Length:Presentation:
11〈a, b | abb=aaa, aaba=b〉
11〈a, b | abb=aaa, abaa=b〉
11〈a, b | abb=aaa, abbb=b〉
11〈a, b | bab=aaa, aaab=b〉
11〈a, b | bab=aaa, aaba=b〉
11〈a, b | bab=aaa, abbb=b〉
11〈a, b | bab=aaa, babb=b〉