NDLI: An upper bound for the power pseudovariety PCS

Content Provider	Springer Nature Link
Author	Kad’ourek, Jiří
Copyright Year	2011
Abstract	It is a celebrated result in finite semigroup theory that the equality of pseudovarieties PG = BG holds, where PG is the pseudovariety of finite monoids generated by all power monoids of finite groups and BG is the pseudovariety of all block groups, that is, the pseudovariety of all finite monoids all of whose regular $${\fancyscript{D}}$$ -classes have the property that the corresponding principal factors are inverse semigroups. Moreover, it is well known that BG = JⓜG, where JⓜG is the pseudovariety of finite monoids generated by the Mal’cev product of the pseudovarieties J and G of all finite $${\fancyscript{J}}$$ -trivial monoids and of all finite groups, respectively. In this paper, a more general kind of finite semigroups is considered; namely, the so-called aggregates of block groups are introduced. It follows that the class AgBG of all aggregates of block groups forms a pseudovariety of finite semigroups. It is next proved that AgBG = JⓜCS, where JⓜCS is the pseudovariety of finite semigroups generated by the Mal’cev product of the pseudovarieties J and CS, whilst, this once, J stands for the pseudovariety of all finite $${\fancyscript{J}}$$ -trivial semigroups and CS stands for the pseudovariety of all finite completely simple semigroups. Furthermore, it is shown that the power pseudovariety PCS, which is the pseudovariety of finite semigroups generated by all power semigroups of finite completely simple semigroups, has the property that $${{\bf PCS}\subseteq{\bf AgBG}}$$ . However, the question whether this inclusion is strict or not is left open.
Ending Page	440
Page Count	30
Starting Page	411
File Format	PDF
ISSN	00269255
e-ISSN	14365081
Journal	Monatshefte für Mathematik
Issue Number	3-4
Volume Number	166
Language	English
Publisher	Springer Vienna
Publisher Date	2011-02-18
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Varieties and pseudovarieties of semigroups Aggregates of block groups Pseudovarieties of finite semigroups Mal’cev products of pseudovarieties of semigroups Power semigroups of finite semigroups Completely simple semigroups Mathematics Power pseudovarieties Block groups
Content Type	Text
Resource Type	Article
Subject	Mathematics

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