Geodesic
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, Tome 6 (2013) no. 2, pp. 18-25

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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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     author = {S. G. Kolesnikov},
     title = {On necessary conditions of regularity of {Sylow} $p$-subgroups of the group $GL_n(\mathbb{Z}_{p^m})$},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
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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, Tome 6 (2013) no. 2, pp. 18-25. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_2_a1/