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Zap. Nauchn. Sem. POMI, 2013, Volume 413, Pages 134–152 (Mi znsl5661)  

This article is cited in 3 scientific papers (total in 3 papers)

Serial group rings of finite groups. $p$-nilpotency

A. V. Kukharev, G. E. Puninski

Belarusian State University, Faculty of Mathematics and Mechanics, Minsk, Belarus

Abstract: We prove that for every finite $p$-nilpotent group $G$ with a cyclic $p$-Sylow subgroup and any field of characteristic $p$, the group ring $FG$ is serial. As a corollary we show that the group ring of a finite group oven an arbitrary field of characteristic $2$ is serial if and only if its $2$-Sylow subgroup is cyclic.

Key words and phrases: finite group, group ring, serial ring.

Full text: PDF file (279 kB)
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English version:
Journal of Mathematical Sciences (New York), 2014, 202:3, 422–433

Bibliographic databases:

Document Type: Article
UDC: 512.553.1+512.553.5
Received: 24.04.2013

Citation: A. V. Kukharev, G. E. Puninski, “Serial group rings of finite groups. $p$-nilpotency”, Problems in the theory of representations of algebras and groups. Part 24, Zap. Nauchn. Sem. POMI, 413, POMI, St. Petersburg, 2013, 134–152; J. Math. Sci. (N. Y.), 202:3 (2014), 422–433

Citation in format AMSBIB
\Bibitem{KukPun13}
\by A.~V.~Kukharev, G.~E.~Puninski
\paper Serial group rings of finite groups. $p$-nilpotency
\inbook Problems in the theory of representations of algebras and groups. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 413
\pages 134--152
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5661}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3073062}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 202
\issue 3
\pages 422--433
\crossref{https://doi.org/10.1007/s10958-014-2052-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919952203}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Kukharev, G. E. Puninski, “Serial group rings of classical groups defined over fields with odd number of elements”, J. Math. Sci. (N. Y.), 232:5 (2018), 693–703  mathnet  crossref  mathscinet
    2. A. V. Kukharev, G. E. Puninski, “Serial group rings of finite simple groups of Lie type”, J. Math. Sci., 233:5 (2018), 695–701  mathnet  crossref
    3. A. V. Kukharev, I. B. Kaigorodov, I. B. Gorshkov, “Kogda gruppovoe koltso prostoi konechnoi gruppy polutsepnoe”, Voprosy teorii predstavlenii algebr i grupp. 32, Zap. nauchn. sem. POMI, 460, POMI, SPb., 2017, 168–189  mathnet
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