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@article{1080712, author = {Kaďourek, Jiří}, article_location = {Wien}, article_number = {34}, doi = {http://dx.doi.org/10.1007/s0060501102855}, keywords = {Pseudovarieties of finite semigroups; Power semigroups of finite semigroups; Power pseudovarieties; Completely simple semigroups; Block groups;Aggregates of block groups; Mal’cev products of pseudovarieties of semigroups}, language = {eng}, issn = {00269255}, journal = {Monatshefte für Mathematik}, title = {An upper bound for the power pseudovariety PCS}, url = {http://link.springer.com/content/pdf/10.1007%2Fs0060501102855}, volume = {166}, year = {2012} }
TY  JOUR ID  1080712 AU  Kaďourek, Jiří PY  2012 TI  An upper bound for the power pseudovariety PCS JF  Monatshefte für Mathematik VL  166 IS  34 SP  411 EP  411 PB  SpringerVerlag SN  00269255 KW  Pseudovarieties of finite semigroups KW  Power semigroups of finite semigroups KW  Power pseudovarieties KW  Completely simple semigroups KW  Block groups;Aggregates of block groups KW  Mal’cev products of pseudovarieties of semigroups UR  http://link.springer.com/content/pdf/10.1007%2Fs0060501102855 N2  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 Dclasses have the property that the corresponding principal factors are inverse semigroups. Moreover, it is well known that BG=JmG, where JmG is the pseudovariety of finite monoids generated by the Mal’cev product of the pseudovarieties J and G of all finite Jtrivial monoids and of all finite groups, respectively. In this paper, a more general kind of finite semigroups is considered; namely, the socalled 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=JmCS, where JmCS 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 Jtrivial 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 PCS is a subclass of AgBG. However, the question whether this inclusion is strict or not is left open. (Recently Karl Auinger has established the equality PCS=AgBG of these pseudovarieties.) ER 
KAĎOUREK, Jiří. An upper bound for the power pseudovariety PCS. \textit{Monatshefte für Mathematik}. Wien: SpringerVerlag, 2012, vol.~166, 34, p.~411440. ISSN~00269255. doi:10.1007/s0060501102855.
