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〈a, b | ab=aa, bb=a〉

Monoid presentation of length 7

Properties

Completion parameters

Complete rewriting system

  1. b4 ⇒ b3
  2. a ⇒ b2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1bb2b3
11bb2b3
bbb2b3b3
b2b2b3b3b3
b3b3b3b3b3

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

8 unique, 1591 total

Length:Presentation:Description:Related:
5 〈a, b | aa=b, bb=1〉 Isomorphic to ℤ4 1419 isomorphic
6 〈a, b | aa=a, bb=a〉 Finite commutative monoid with 4 elements 37 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 | 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

16 total

Length:Presentation:
7〈a, b | ab=a, bbb=a〉
8〈a, b | aa=b, aaa=bb〉
8〈a, b | aa=b, aab=ab〉
8〈a, b | aa=b, aab=ba〉
8〈a, b | aa=b, aba=ab〉
8〈a, b | ab=a, bbb=ab〉
9〈a, b | aaa=b, aaaa=b〉
9〈a, b | aa=b, aaaa=ab〉
9〈a, b | aa=b, aab=aaa〉
9〈a, b | aa=b, aba=aaa〉
9〈a, b | ab=a, bbb=abb〉
10〈a, b | aa=b, aaaa=aaa〉
10〈a, b | ab=a, abbb=bbb〉
11〈a, b | aaa=b, aaaa=aaa〉
11〈a, b | aab=a, abbb=bbb〉
11〈a, b | ab=a, abbbb=bbb〉