KAĎOUREK, Jiří. An upper bound for the power pseudovariety PCS. Monatshefte für Mathematik. Wien: Springer-Verlag, 2012, vol. 166, 3-4, p. 411-440. ISSN 0026-9255. doi:10.1007/s00605-011-0285-5.
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Basic information
Original name An upper bound for the power pseudovariety PCS
Authors KAĎOUREK, Jiří (203 Czech Republic, guarantor, belonging to the institution).
Edition Monatshefte für Mathematik, Wien, Springer-Verlag, 2012, 0026-9255.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Austria
Confidentiality degree is not subject to a state or trade secret
WWW URL
Impact factor Impact factor: 0.698
RIV identification code RIV/00216224:14310/12:00062631
Organization unit Faculty of Science
Doi http://dx.doi.org/10.1007/s00605-011-0285-5
UT WoS 000304564700010
Keywords in English 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
Tags AKR, rivok
Tags International impact, Reviewed
Changed by Changed by: Ing. Andrea Mikešková, učo 137293. Changed: 22/4/2013 15:06.
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 D-classes 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 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=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 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 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.)
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MSM0021622409, plan (intention)Name: Matematické struktury a jejich fyzikální aplikace
Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures and their physical applications
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