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〈a, b | aa=a, bb=a〉

Monoid presentation of length 6

Properties

Completion parameters

Complete rewriting system

  1. b4 ⇒ b2
  2. a ⇒ b2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1bb2b3
11bb2b3
bbb2b3b2
b2b2b3b2b3
b3b3b2b3b2

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

8 unique, 1570 total

Length:Presentation:Description:Related:
5 〈a, b | aa=b, bb=1〉 Isomorphic to ℤ4 1419 isomorphic
6 〈a, b | aa=b, bb=a〉 Finite commutative monoid with 4 elements 72 isomorphic
7 〈a, b | ab=aa, ba=b〉 Finite non-commutative monoid with 4 elements 8 isomorphic, 6 anti-isomorphic
7 〈a, b | ab=aa, bb=a〉 Finite commutative monoid with 4 elements 16 isomorphic
7 〈a, b | aa=a, abb=b〉 Finite non-commutative monoid with 4 elements 14 isomorphic
7 〈a, b | ab=a, bb=aa〉 Finite commutative monoid with 4 elements 17 isomorphic
9 〈a, b | aa=a, abbba=b〉 Finite commutative monoid with 4 elements 8 isomorphic
10 〈a, b | aaa=aa, abba=b〉 Finite commutative monoid with 4 elements 2 isomorphic

Other isomorphic instances

37 total

Length:Presentation:
7〈a, b | aa=b, aab=b〉
7〈a, b | aa=b, aba=b〉
7〈a, b | aa=a, bb=aa〉
7〈a, b | aa=b, bb=aa〉
8〈a, b | ab=aa, aaa=b〉
8〈a, b | ab=aa, aab=b〉
8〈a, b | ab=aa, aba=b〉
8〈a, b | ab=aa, abb=b〉
8〈a, b | aa=b, aaaa=b〉
8〈a, b | aa=a, aaa=bb〉
8〈a, b | aa=b, aab=aa〉
8〈a, b | aa=b, aba=aa〉
9〈a, b | aab=aa, aba=b〉
9〈a, b | aa=a, aaaa=bb〉
9〈a, b | aa=b, aaaa=aa〉
10〈a, b | aab=aa, aabb=b〉
10〈a, b | aab=aa, abab=b〉
10〈a, b | aab=aa, abba=b〉
10〈a, b | aba=aa, abba=b〉
10〈a, b | aaa=b, aaaa=aa〉
10〈a, b | aab=a, aabb=bb〉
10〈a, b | aab=a, abab=bb〉
10〈a, b | aab=a, abba=bb〉
10〈a, b | aab=b, aaab=aa〉
10〈a, b | aba=b, aaab=aa〉
10〈a, b | aba=b, aaba=aa〉
10〈a, b | aa=a, aaaaa=bb〉
11〈a, b | aab=aa, aabbb=b〉
11〈a, b | aab=aa, ababb=b〉
11〈a, b | aab=aa, abbab=b〉
11〈a, b | aab=aa, abbba=b〉
11〈a, b | aba=aa, abbba=b〉
11〈a, b | aab=b, aaaab=aa〉
11〈a, b | aba=b, aaaab=aa〉
11〈a, b | aba=b, aaaba=aa〉
11〈a, b | aba=b, aabaa=aa〉
11〈a, b | aa=a, aaaaaa=bb〉