Embedding in a nite 2-generator semigroup
نویسنده
چکیده
In this paper we will be on erned with the possibility of embedding a nite semigroup S into a nite 2-generated semigroup T that shares properties with S. In parti ular we show that any nite orthodox semigroup S may be embedded in a nite orthodox semigroup T generated by two group elements and that any nite orthodox monoid S1 may be embedded as a semigroup into a nite 2-generated orthodox monoid T whose subband of idempotents satis es the same semigroup identities. Prior to that we prove that if S1 is a nite monoid whose idempotents E(S1) form a subsemigroup, then S1 may be embedded in a 2-generated nite monoid T whose idempotents also form a subsemigroup and belong to the same variety of bands. For ba kground on semigroups we refer to standard texts su h as [4℄ or [5℄.
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