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〈a, b | ab=aa, baaa=bb〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a5 ⇒ a3
  2. ab ⇒ a2
  3. b2 ⇒ ba3

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3ba4
11aba2baa3ba2a4ba3ba4
aaa2a2a3a3a4a4a3a3a4
bbbaba3ba2ba4ba3ba3ba4ba4ba3
a2a2a3a3a4a4a3a3a4a4a3
bababa2ba2ba3ba3ba4ba4ba3ba3ba4
a3a3a4a4a3a3a4a4a3a3a4
ba2ba2ba3ba3ba4ba4ba3ba3ba4ba4ba3
a4a4a3a3a4a4a3a3a4a4a3
ba3ba3ba4ba4ba3ba3ba4ba4ba3ba3ba4
ba4ba4ba3ba3ba4ba4ba3ba3ba4ba4ba3

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

37 unique, 916 total

Length:Presentation:Description:Related:
7 〈a, b | aa=1, abbb=b〉 Finite non-commutative monoid with 10 elements 51 isomorphic, 34 anti-isomorphic
8 〈a, b | aaa=b, abbb=1〉 Isomorphic to ℤ10 536 isomorphic
8 〈a, b | bb=aa, aba=a〉 Finite non-commutative monoid with 10 elements 1 isomorphic
8 〈a, b | bb=aa, aba=b〉 Finite non-commutative monoid with 10 elements 1 isomorphic
8 〈a, b | aa=a, bbb=ab〉 Finite non-commutative monoid with 10 elements 3 isomorphic
9 〈a, b | aab=bb, bba=a〉 Finite non-commutative monoid with 10 elements 6 isomorphic
9 〈a, b | aaa=b, abbb=a〉 Finite commutative monoid with 10 elements 59 isomorphic
9 〈a, b | aaa=b, abbb=b〉 Finite commutative monoid with 10 elements 35 isomorphic
9 〈a, b | bb=aa, aba=aa〉 Finite non-commutative monoid with 10 elements 1 isomorphic
9 〈a, b | aa=a, bbbbb=a〉 Finite commutative monoid with 10 elements 17 isomorphic
9 〈a, b | aa=b, bbbbb=b〉 Finite commutative monoid with 10 elements 57 isomorphic
10 〈a, b | aaaa=b, aabb=b〉 Finite commutative monoid with 10 elements 20 isomorphic
10 〈a, b | aaa=bb, abb=ab〉 Finite non-commutative monoid with 10 elements 2 isomorphic
10 〈a, b | aaa=bb, abb=ba〉 Finite non-commutative monoid with 10 elements
10 〈a, b | aab=aa, aba=bb〉 Finite non-commutative monoid with 10 elements
10 〈a, b | aaa=b, abbb=bb〉 Finite commutative monoid with 10 elements 3 isomorphic
10 〈a, b | aab=a, baaa=bb〉 Finite non-commutative monoid with 10 elements
10 〈a, b | ab=aa, baaaa=b〉 Finite non-commutative monoid with 10 elements 14 isomorphic
10 〈a, b | aa=a, abbbbb=b〉 Finite non-commutative monoid with 10 elements 5 isomorphic
10 〈a, b | ab=a, baaaa=bb〉 Finite non-commutative monoid with 10 elements 4 isomorphic
11 〈a, b | aaab=baa, abab=1〉 Finite non-Abelian group with 10 elements 3 isomorphic
11 〈a, b | aaaa=aa, abba=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aaaa=ab, baaa=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aaaa=bb, aaab=a〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aaaa=bb, aaab=b〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aabb=aa, bbbb=a〉 Finite commutative monoid with 10 elements 3 isomorphic
11 〈a, b | abab=aa, baab=b〉 Finite non-commutative monoid with 10 elements 4 isomorphic
11 〈a, b | aab=bb, aaaaa=b〉 Finite commutative monoid with 10 elements 7 isomorphic
11 〈a, b | aab=bb, abbbb=a〉 Finite commutative monoid with 10 elements 5 isomorphic
11 〈a, b | aba=aa, aaaab=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aab=b, abbbb=aa〉 Finite commutative monoid with 10 elements 5 isomorphic
11 〈a, b | aaa=b, abbb=bbb〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aab=a, bbbb=bab〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aab=b, aaaa=baa〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aba=b, aaaa=bbb〉 Finite commutative monoid with 10 elements
11 〈a, b | ab=a, bbbb=baaa〉 Finite non-commutative monoid with 10 elements
11 〈a, b | ab=a, bbbb=bbaa〉 Finite non-commutative monoid with 10 elements

Other isomorphic instances

3 total

Length:Presentation:
10〈a, b | ab=aa, baab=bb〉
10〈a, b | ab=aa, baba=bb〉
10〈a, b | ab=aa, babb=bb〉