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〈a, b | ab=aa, aaaaa=bb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a6 ⇒ a3
  2. ba3 ⇒ a4
  3. ab ⇒ a2
  4. b2 ⇒ a5

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4a5
11aba2baa3ba2a4a5
aaa2a2a3a3a4a4a5a3
bbbaa5ba2a3a4a4a5a3
a2a2a3a3a4a4a5a5a3a4
bababa2ba2a4a4a5a5a3a4
a3a3a4a4a5a5a3a3a4a5
ba2ba2a4a4a5a5a3a3a4a5
a4a4a5a5a3a3a4a4a5a3
a5a5a3a3a4a4a5a5a3a4

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

38 unique, 927 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 | abb=aaa, aaab=b〉 Finite commutative monoid with 9 elements 7 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=a, bbbbb=baa〉 Finite non-commutative monoid with 9 elements

Other isomorphic instances

15 total

Length:Presentation:
11〈a, b | ab=aa, aaaab=bb〉
11〈a, b | ab=aa, aaaba=bb〉
11〈a, b | ab=aa, aaabb=bb〉
11〈a, b | ab=aa, aabaa=bb〉
11〈a, b | ab=aa, aabab=bb〉
11〈a, b | ab=aa, aabba=bb〉
11〈a, b | ab=aa, aabbb=bb〉
11〈a, b | ab=aa, abaaa=bb〉
11〈a, b | ab=aa, abaab=bb〉
11〈a, b | ab=aa, ababa=bb〉
11〈a, b | ab=aa, ababb=bb〉
11〈a, b | ab=aa, abbaa=bb〉
11〈a, b | ab=aa, abbab=bb〉
11〈a, b | ab=aa, abbba=bb〉
11〈a, b | ab=aa, abbbb=bb〉