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Journal of Siberian Federal University. Mathematics & Physics, 2011, Volume 4, Issue 4, Pages 489–497
(Mi jsfu207)
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This article is cited in 1 scientific paper (total 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.
Received: 31.05.2011 Received in revised form: 25.08.2011 Accepted: 10.09.2011
Citation:
Sergey G. Kolesnikov, Nikolay V. Maltsev, “On the regularity Sylow's $p$-subgroups of symplectic and orthogonal groups over ring $\mathbb Z/p^m\mathbb Z$”, J. Sib. Fed. Univ. Math. Phys., 4:4 (2011), 489–497
Linking options:
https://www.mathnet.ru/eng/jsfu207 https://www.mathnet.ru/eng/jsfu/v4/i4/p489
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