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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2013, Volume 16, Issue 2, Pages 201–216 (Mi adm447)

RESEARCH ARTICLE

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

A. Kukharev, G. Puninski

Faculty of Mechanics and Mathematics, Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus

Abstract: We prove that for any finite $p$-solvable group $G$ with a cyclic $p$-Sylow subgroup and any field $F$ of characteristic $p$, the group ring $FG$ is serial. As a corollary for an arbitrary field we will produce a list of all groups of order $\leq 100$ whose group rings are serial.

Keywords: Serial ring, group ring, $p$-solvable group.

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MSC: 20C05,16L30
Revised: 13.09.2013
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Citation: A. Kukharev, G. Puninski, “Serial group rings of finite groups. $p$-solvability”, Algebra Discrete Math., 16:2 (2013), 201–216

Citation in format AMSBIB
\Bibitem{KukPun13} \by A.~Kukharev, G.~Puninski \paper Serial group rings of finite groups. $p$-solvability \jour Algebra Discrete Math. \yr 2013 \vol 16 \issue 2 \pages 201--216 \mathnet{http://mi.mathnet.ru/adm447} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3186084} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yu. V. Volkov, A. V. Kukharev, G. E. Puninski, “The seriality of the group ring of a finite group depends only on the characteristic of the field”, J. Math. Sci. (N. Y.), 209:4 (2015), 515–521
2. A. V. Kukharev, G. E. Puninski, “Serial group rings of finite groups. Sporadic simple groups and Suzuki groups”, J. Math. Sci. (N. Y.), 219:4 (2016), 539–552
3. Andrei Kukharev, Gena Puninski, “Serial group rings of finite groups. General linear and close groups”, Algebra Discrete Math., 20:1 (2015), 115–125
4. A. V. Kukharev, G. E. Puninski, “Serial group rings of finite simple groups of Lie type”, J. Math. Sci., 233:5 (2018), 695–701
5. A. V. Kukharev, I. B. Kaygorodov, I. B. Gorshkov, “When the group ring of a simple finite group is serial”, J. Math. Sci. (N. Y.), 240:4 (2019), 481–493
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