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Fundam. Prikl. Mat., 2016, Volume 21, Issue 1, Pages 135–144 (Mi fpm1708)  

This article is cited in 1 scientific paper (total in 1 paper)

Serial group rings of finite simple groups of Lie type

A. V. Kukhareva, G. E. Puninskib

a Vitebsk State University named after P. M. Masherov
b Belarusian State University, Minsk

Abstract: Suppose that $F$ is a field whose characteristic $p$ divides the order of a finite group $G$. It is shown that if $G$ is one of the groups $ ^3 D_4(q)$, $E_6(q)$, $ ^2E_6(q)$, $E_7(q)$, $E_8(q)$, $F_4(q)$, $ ^2F_4(q)$, or $ ^2G_2(q)$, then the group ring $FG$ is not serial. If $G= G_2(q^2)$, then the ring $FG$ is serial if and only if either $p>2$ divides $q^2-1$, or $p=7$ divides $q^2 + \sqrt{3}q + 1$ but $49$ does not divide this number.

Funding Agency Grant Number
Belarusian Republican Foundation for Fundamental Research Ф15РМ-025


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English version:
Journal of Mathematical Sciences (New York), 2018, 233:5, 695–701

UDC: 512.552.7+512.547.23

Citation: A. V. Kukharev, G. E. Puninski, “Serial group rings of finite simple groups of Lie type”, Fundam. Prikl. Mat., 21:1 (2016), 135–144; J. Math. Sci., 233:5 (2018), 695–701

Citation in format AMSBIB
\Bibitem{KukPun16}
\by A.~V.~Kukharev, G.~E.~Puninski
\paper Serial group rings of finite simple groups of Lie type
\jour Fundam. Prikl. Mat.
\yr 2016
\vol 21
\issue 1
\pages 135--144
\mathnet{http://mi.mathnet.ru/fpm1708}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 233
\issue 5
\pages 695--701
\crossref{https://doi.org/10.1007/s10958-018-3957-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85050933345}


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    This publication is cited in the following articles:
    1. 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  mathnet  crossref
  • Фундаментальная и прикладная математика
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