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〈a, b | aba=aa, baa=b〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. a4 ⇒ a2
  2. ba2 ⇒ b
  3. ab ⇒ a3
  4. b2 ⇒ b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3
11aba2baa3
aaa2a3a3a2a2
bbbabbbaba
a2a2a3a2a2a3a3
bababbababb
a3a3a2a3a3a2a2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

25 unique, 1925 total

Length:Presentation:Description:Related:
6 〈a, b | ab=aa, bb=1〉 Finite non-commutative monoid with 6 elements 22 isomorphic
6 〈a, b | aaa=1, abb=1〉 Isomorphic to ℤ6 1373 isomorphic
6 〈a, b | aa=1, abb=b〉 Finite non-commutative monoid with 6 elements 30 isomorphic
7 〈a, b | ab=aa, bb=b〉 Finite non-commutative monoid with 6 elements
7 〈a, b | aa=a, bbb=a〉 Finite commutative monoid with 6 elements 49 isomorphic
7 〈a, b | aa=b, bbb=a〉 Finite commutative monoid with 6 elements 61 isomorphic
7 〈a, b | aa=b, bbb=b〉 Finite commutative monoid with 6 elements 55 isomorphic
7 〈a, b | aa=1, abab=b〉 Finite non-commutative monoid with 6 elements 31 isomorphic, 22 anti-isomorphic
8 〈a, b | ab=aa, baa=b〉 Finite non-commutative monoid with 6 elements 4 isomorphic
8 〈a, b | ab=aa, bbb=a〉 Finite commutative monoid with 6 elements 46 isomorphic
8 〈a, b | aa=a, abbb=b〉 Finite non-commutative monoid with 6 elements 19 isomorphic
8 〈a, b | aa=a, aab=bb〉 Finite non-commutative monoid with 6 elements 3 isomorphic
8 〈a, b | ab=a, baa=bb〉 Finite non-commutative monoid with 6 elements 12 isomorphic, 1 anti-isomorphic
9 〈a, b | abba=b, baba=1〉 Finite non-Abelian group with 6 elements 66 isomorphic
9 〈a, b | aaa=aa, abb=b〉 Finite non-commutative monoid with 6 elements 5 isomorphic
9 〈a, b | aab=bb, abb=a〉 Finite commutative monoid with 6 elements 13 isomorphic
9 〈a, b | abb=aa, bbb=a〉 Finite commutative monoid with 6 elements 49 isomorphic
9 〈a, b | ab=a, aaaa=bb〉 Finite commutative monoid with 6 elements 14 isomorphic
9 〈a, b | ab=a, bbbb=aa〉 Finite commutative monoid with 6 elements 5 isomorphic
9 〈a, b | ab=a, bbbb=ba〉 Finite non-commutative monoid with 6 elements 2 isomorphic
9 〈a, b | ab=a, bbb=aaa〉 Finite commutative monoid with 6 elements 9 isomorphic
9 〈a, b | ab=a, bbb=bba〉 Finite non-commutative monoid with 6 elements 3 isomorphic
10 〈a, b | aba=aa, aabb=b〉 Finite non-commutative monoid with 6 elements 5 isomorphic
10 〈a, b | aab=b, aaba=aa〉 Finite non-commutative monoid with 6 elements 1 isomorphic
11 〈a, b | aa=a, abbbbba=b〉 Finite commutative monoid with 6 elements