Back

〈a, b | aab=a, baaaa=bb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a6 ⇒ a
  2. ab ⇒ a5
  3. b2 ⇒ ba4

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3a5ba4ba5
11aba2baa3ba2a4ba3a5ba4ba5
aaa2a5a3aa4a2a5a3aa4a5
bbbaba4ba2ba5ba3baba4ba2ba5ba3ba4
a2a2a3aa4a2a5a3aa4a2a5a
bababa2ba5ba3baba4ba2ba5ba3baba4ba5
a3a3a4a2a5a3aa4a2a5a3aa2
ba2ba2ba3baba4ba2ba5ba3baba4ba2ba5ba
a4a4a5a3aa4a2a5a3aa4a2a3
ba3ba3ba4ba2ba5ba3baba4ba2ba5ba3baba2
a5a5aa4a2a5a3aa4a2a5a3a4
ba4ba4ba5ba3baba4ba2ba5ba3baba4ba2ba3
ba5ba5baba4ba2ba5ba3baba4ba2ba5ba3ba4

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

51 unique, 659 total

Length:Presentation:Description:Related:
7 〈a, b | aab=a, bbb=1〉 Finite non-commutative monoid with 12 elements 8 isomorphic, 12 anti-isomorphic
7 〈a, b | ab=aa, bbb=1〉 Finite non-commutative monoid with 12 elements 9 isomorphic
8 〈a, b | aba=ab, bbb=1〉 Finite non-commutative monoid with 12 elements
8 〈a, b | aaaa=1, abbb=1〉 Isomorphic to ℤ12 325 isomorphic
8 〈a, b | ab=aa, bbb=b〉 Finite non-commutative monoid with 12 elements
8 〈a, b | aaa=1, aabb=b〉 Finite non-commutative monoid with 12 elements 16 isomorphic
9 〈a, b | aab=bb, aba=a〉 Finite non-commutative monoid with 12 elements 2 isomorphic
9 〈a, b | aba=b, aaabb=1〉 Finite non-Abelian group with 12 elements 19 isomorphic
9 〈a, b | aaa=a, bbbb=a〉 Finite commutative monoid with 12 elements 6 isomorphic
9 〈a, b | aaa=b, bbbb=a〉 Finite commutative monoid with 12 elements 27 isomorphic
9 〈a, b | aaa=b, bbbb=b〉 Finite commutative monoid with 12 elements 23 isomorphic
9 〈a, b | ab=aa, bbb=bb〉 Finite non-commutative monoid with 12 elements
9 〈a, b | aaa=1, aabab=b〉 Finite non-commutative monoid with 12 elements 8 isomorphic, 4 anti-isomorphic
10 〈a, b | bab=aba, aabb=1〉 Finite non-Abelian group with 12 elements 4 isomorphic
10 〈a, b | aaa=aa, bbbb=a〉 Finite commutative monoid with 12 elements
10 〈a, b | aaa=ab, bbbb=a〉 Finite commutative monoid with 12 elements 7 isomorphic
10 〈a, b | aaa=bb, bbbb=a〉 Finite commutative monoid with 12 elements 43 isomorphic
10 〈a, b | aab=bb, abba=a〉 Finite non-commutative monoid with 12 elements 6 isomorphic
10 〈a, b | aaa=ab, bab=bb〉 Finite non-commutative monoid with 12 elements 1 isomorphic
10 〈a, b | aaa=a, aaab=bb〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aaa=b, bbbb=bb〉 Finite commutative monoid with 12 elements 4 isomorphic
10 〈a, b | aab=a, bbbb=ba〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aab=a, bbbb=bb〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aba=a, bbbb=ab〉 Finite non-commutative monoid with 12 elements
10 〈a, b | ab=aa, bbaa=bb〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaaa=aa, abab=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aaab=bb, aaba=a〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=aaa, baaa=b〉 Finite non-commutative monoid with 12 elements 4 isomorphic
11 〈a, b | aab=aaa, bbbb=a〉 Finite commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=ba, ababbb=1〉 Finite non-Abelian group with 12 elements 5 isomorphic
11 〈a, b | aaa=aa, abbbb=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aaa=ab, aabb=bb〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaa=bb, aabb=ab〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaa=bb, aabb=ba〉 Finite non-commutative monoid with 12 elements 1 isomorphic
11 〈a, b | aab=aa, abab=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aab=bb, aaaa=ab〉 Finite non-commutative monoid with 12 elements 1 isomorphic
11 〈a, b | aab=bb, aaaa=ba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aba=bb, aabb=aa〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aba=b, bbbbb=aa〉 Finite commutative monoid with 12 elements
11 〈a, b | aaa=b, bbbb=abb〉 Finite commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=a, bbaa=bbb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aab=b, aaaa=bba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=aa, baaaaa=b〉 Finite non-commutative monoid with 12 elements 30 isomorphic
11 〈a, b | bb=aa, aaaaab=a〉 Finite commutative monoid with 12 elements 15 isomorphic
11 〈a, b | ab=aa, baaaa=bb〉 Finite non-commutative monoid with 12 elements 7 isomorphic
11 〈a, b | bb=aa, aaaa=aba〉 Finite non-commutative monoid with 12 elements 4 isomorphic
11 〈a, b | bb=aa, aaab=aba〉 Finite non-commutative monoid with 12 elements 3 isomorphic
11 〈a, b | bb=aa, abab=aba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aa=a, abbbbbb=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=a, baaaaa=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=a, bbaaa=bbb〉 Finite non-commutative monoid with 12 elements