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The Bulletin of Irkutsk State University. Series Mathematics, 2013, Volume 6, Issue 2, Pages 18–25 (Mi iigum12)  

On necessary conditions of regularity of Sylow $p$-subgroups of the group $GL_n(\mathbb{Z}_{p^m})$

S. G. Kolesnikovab

a Siberian Federal University, 79, Svobodny av., Krasnoyarsk, 660041
b M. F. Reshetnev Siberian State Aerospace University

Abstract: In connect to B. Vehrfritz's problem 8.3 from Kourovka notebook we prooved that Sylow $p$-subgroup of group $GL_n(\mathbb{Z}_{p^m})$ when $n\leqslant (p-1)/2$ satisfies well-known necessary coditions of regularity.

Keywords: regular $p$-group; linear group; Sylow subgroup.

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UDC: 512.517

Citation: S. G. Kolesnikov, “On necessary conditions of regularity of Sylow $p$-subgroups of the group $GL_n(\mathbb{Z}_{p^m})$”, The Bulletin of Irkutsk State University. Series Mathematics, 6:2 (2013), 18–25

Citation in format AMSBIB
\Bibitem{Kol13}
\by S.~G.~Kolesnikov
\paper On necessary conditions of regularity of Sylow $p$-subgroups of the group $GL_n(\mathbb{Z}_{p^m})$
\jour The Bulletin of Irkutsk State University. Series Mathematics
\yr 2013
\vol 6
\issue 2
\pages 18--25
\mathnet{http://mi.mathnet.ru/iigum12}


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