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〈a, b | ab=a, bbaaa=bbb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a4 ⇒ a
  2. ab ⇒ a
  3. b3 ⇒ b2a3

Idempotents

4 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2aba3b2a2b2a3
11aba2bab2a3ba2b2aba3b2a2b2a3
aaa2aa3a2aaa3a2aa3a
bbbab2ba2b2ab2a3ba3b2a2b2ab2a3b2a2b2a3
a2a2a3a2aa3a2a2aa3a2aa2
bababa2baba3ba2bababa3ba2baba3ba
b2b2b2ab2a3b2a2b2ab2a3b2a3b2a2b2ab2a3b2a2b2a3
a3a3aa3a2aa3a3a2aa3a2a3
ba2ba2ba3ba2baba3ba2ba2baba3ba2baba2
b2ab2ab2a2b2ab2a3b2a2b2ab2ab2a3b2a2b2ab2a3b2a
ba3ba3baba3ba2baba3ba3ba2baba3ba2ba3
b2a2b2a2b2a3b2a2b2ab2a3b2a2b2a2b2ab2a3b2a2b2ab2a2
b2a3b2a3b2ab2a3b2a2b2ab2a3b2a3b2a2b2ab2a3b2a2b2a3

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 | 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