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〈a, b | aba=aa, aabb=b〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a4 ⇒ a2
  2. ba ⇒ a3
  3. a2b ⇒ b
  4. b2 ⇒ b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2aba3
11aba2aba3
aaa2aba3ba2
bba3ba2aba3
a2a2a3ba2aba3
ababa2aba3ba2
a3a3a2aba3ba2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

25 unique, 1920 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 | aba=aa, baa=b〉 Finite non-commutative monoid with 6 elements
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 | 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

Other isomorphic instances

5 total

Length:Presentation:
10〈a, b | aba=aa, abab=b〉
11〈a, b | aba=aa, aabbb=b〉
11〈a, b | aba=aa, ababb=b〉
11〈a, b | aba=aa, abbab=b〉
11〈a, b | aab=b, aaaba=aa〉