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〈a, b | aaa=bb, aab=ba〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a7 ⇒ a4
  2. a6b ⇒ a3b
  3. ba ⇒ a2b
  4. b2 ⇒ a3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3a5ba4a6ba5
11aba2baa3ba2a4ba3a5ba4a6ba5
aaa2ba2a3ba3a4ba4a5ba5a6ba3a4ba4
bbbaa3ba2a4ba3a5ba4a6ba5a4ba3a5
a2a2a3ba4a4ba5a5ba3a6ba4a4ba5a5ba3
bababa2a5ba3a6ba4a4ba5a5ba3a6ba4a4
a3a3a4ba3a5ba4a6ba5a4ba3a5ba4a6ba5
ba2ba2ba3a4ba4a5ba5a6ba3a4ba4a5ba5a6
a4a4a5ba5a6ba3a4ba4a5ba5a6ba3a4ba4
ba3ba3ba4a6ba5a4ba3a5ba4a6ba5a4ba3a5
a5a5a6ba4a4ba5a5ba3a6ba4a4ba5a5ba3
ba4ba4ba5a5ba3a6ba4a4ba5a5ba3a6ba4a4
a6a6a4ba3a5ba4a6ba5a4ba3a5ba4a6ba5
ba5ba5ba3a4ba4a5ba5a6ba3a4ba4a5ba5a6

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

33 unique, 303 total

Length:Presentation:Description:Related:
9 〈a, b | aaaa=b, abbb=1〉 Isomorphic to ℤ13 189 isomorphic
9 〈a, b | aba=b, baab=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
10 〈a, b | aaaa=b, abbb=a〉 Finite commutative monoid with 13 elements 10 isomorphic
10 〈a, b | aaaa=b, abbb=b〉 Finite commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaab=b, abba=a〉 Finite non-commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aaa=ab, babb=b〉 Finite non-commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaa=ab, bba=bb〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=ab, bbb=ab〉 Finite non-commutative monoid with 13 elements 1 isomorphic
10 〈a, b | aaa=ab, bbb=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=b, abbbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aab=b, abbba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
10 〈a, b | bb=aa, aaab=ba〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=aa, bbbb=a〉 Finite commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=ab, bbbb=a〉 Finite commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaab=bb, bbbb=a〉 Finite commutative monoid with 13 elements 14 isomorphic
11 〈a, b | aaab=b, aabba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaba=b, babbb=a〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=bb, aabbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=ab, abbb=bb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, abbb=ba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, babb=ab〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=ab, bbbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbbb=aa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aba=bb, abbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ab, bbb=aaa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbb=aaa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbbbb=a〉 Finite commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=b, ababba=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=a, baaa=bbb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbb=bba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | ab=aa, aaaa=bbb〉 Finite non-commutative monoid with 13 elements 7 isomorphic
11 〈a, b | ab=aa, baaa=bbb〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | ab=a, baaaaaa=b〉 Finite non-commutative monoid with 13 elements