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JOURNALS // Journal of Siberian Federal University. Mathematics & Physics // Archive

J. Sib. Fed. Univ. Math. Phys., 2011 Volume 4, Issue 4, Pages 489–497 (Mi jsfu207)

This article is cited in 1 paper

On the regularity Sylow's $p$-subgroups of symplectic and orthogonal groups over ring $\mathbb Z/p^m\mathbb Z$

Sergey G. Kolesnikova, Nikolay V. Maltsevb

a Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia
b Institute of Basic Training, Siberian Federal University, Krasnoyarsk, Russia

Abstract: For symplectic $Sp_{2n}(\mathbb Z/p^m\mathbb Z)$ and orthogonal $O^+_{2n}(\mathbb Z/p^m\mathbb Z)$ groups over residue ring of integers $\mathbb Z/p^m\mathbb Z,$ $p$ – prime integer, $m\ge1,$ we investigate analog Wehrfritz's question 8.3 from Kourovka notebook: for which $n,m,p$ Sylow $p$-subgroups of groups $Sp_{2n}(\mathbb Z/p^m\mathbb Z)$ and $O^+_{2n}(\mathbb Z/p^m\mathbb Z)$ are regular?

Keywords: regular $p$-group, symplectic group, orthogonal group, Sylow subgroup.

UDC: 512.54

Received: 31.05.2011
Received in revised form: 25.08.2011
Accepted: 10.09.2011



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