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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2006 Volume 47, Number 6, Pages 1289–1295 (Mi smj934)

This article is cited in 6 papers

On the regular Sylow $p$-subgroups of Chevalley groups over $\mathbb Z_{p^m}$

S. G. Kolesnikov

Krasnoyarsk State University

Abstract: We prove that a Sylow $p$-subgroup of the general linear group of dimension $n$ over the residue ring modulo $p^m$ is regular for $n^2<p$ and powerful if and only if $n=2$ and $m=1$. We obtain similar results for the Sylow $p$-subgroups of normal types over the same ring.

Keywords: regular $p$-group, powerful $p$-group, Sylow $p$-subgroup.

UDC: 519.54

Received: 14.02.2006


 English version:
Siberian Mathematical Journal, 2006, 47:6, 1054–1059

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© Steklov Math. Inst. of RAS, 2025