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〈a, b | ab=a, baa=bb〉

Monoid presentation of length 8

Properties

Completion parameters

Complete rewriting system

  1. a3 ⇒ a
  2. ab ⇒ a
  3. b2 ⇒ ba2

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2baba2
11aba2baba2
aaa2aaa2a
bbbaba2ba2baba2
a2a2aa2a2aa2
bababa2bababa2ba
ba2ba2baba2ba2baba2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

25 unique, 1912 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
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 | 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

Other isomorphic instances

12 total

Length:Presentation:
9〈a, b | ab=a, baab=bb〉
9〈a, b | ab=a, baba=bb〉
10〈a, b | ab=a, baabb=bb〉
10〈a, b | ab=a, babab=bb〉
10〈a, b | ab=a, babba=bb〉
11〈a, b | abab=aa, babb=b〉
11〈a, b | abab=aa, bbab=b〉
11〈a, b | abab=aa, bbba=b〉
11〈a, b | ab=a, baabbb=bb〉
11〈a, b | ab=a, bababb=bb〉
11〈a, b | ab=a, babbab=bb〉
11〈a, b | ab=a, babbba=bb〉

Other anti-isomorphic instances

1 total

Length:Presentation:
11〈a, b | abba=aa, abbb=b〉