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

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.

Full text: PDF file (180 kB)
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UDC: 512.54
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

Citation in format AMSBIB
\Bibitem{KolMal11}
\by Sergey~G.~Kolesnikov, Nikolay~V.~Maltsev
\paper On the regularity Sylow's $p$-subgroups of symplectic and orthogonal groups over ring $\mathbb Z/p^m\mathbb Z$
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2011
\vol 4
\issue 4
\pages 489--497
\mathnet{http://mi.mathnet.ru/jsfu207}


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    This publication is cited in the following articles:
    1. S. G. Kolesnikov, “O neobkhodimykh usloviyakh regulyarnosti silovskoi $p$-podgruppy gruppy $GL_n(\mathbb{Z}_{p^m})$”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 6:2 (2013), 18–25  mathnet
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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