Back

〈a, b | aab=bb, abba=a〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a6 ⇒ a
  2. ba ⇒ a3
  3. b2 ⇒ a2b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2aba3a2ba4a3ba5a4ba5b
11aba2aba3a2ba4a3ba5a4ba5b
aaa2aba3a2ba4a3ba5a4baa5bab
bba3a2ba4a3ba5a4baa5ba2aba2b
a2a2a3a2ba4a3ba5a4baa5ba2aba2b
ababa4a3ba5a4baa5ba2aba3a2ba3b
a3a3a4a3ba5a4baa5ba2aba3a2ba3b
a2ba2ba5a4baa5ba2aba3a2ba4a3ba4b
a4a4a5a4baa5ba2aba3a2ba4a3ba4b
a3ba3baa5ba2aba3a2ba4a3ba5a4ba5b
a5a5aa5ba2aba3a2ba4a3ba5a4ba5b
a4ba4ba2aba3a2ba4a3ba5a4baa5bab
a5ba5ba3a2ba4a3ba5a4baa5ba2aba2b

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

51 unique, 653 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 | 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 | aab=a, baaaa=bb〉 Finite non-commutative monoid with 12 elements
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

Other isomorphic instances

6 total

Length:Presentation:
10〈a, b | aab=bb, baba=a〉
10〈a, b | aab=bb, bbaa=a〉
11〈a, b | aab=bb, aaaba=a〉
11〈a, b | aab=bb, aabaa=a〉
11〈a, b | aab=bb, abaaa=a〉
11〈a, b | aab=bb, baaaa=a〉