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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{IIGUM_2013_6_2_a1,
     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},
     pages = {18--25},
     year = {2013},
     volume = {6},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2013_6_2_a1/}
}
TY  - JOUR
AU  - S. G. Kolesnikov
TI  - On necessary conditions of regularity of Sylow $p$-subgroups of the group $GL_n(\mathbb{Z}_{p^m})$
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2013
SP  - 18
EP  - 25
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2013_6_2_a1/
LA  - ru
ID  - IIGUM_2013_6_2_a1
ER  - 
%0 Journal Article
%A S. G. Kolesnikov
%T On necessary conditions of regularity of Sylow $p$-subgroups of the group $GL_n(\mathbb{Z}_{p^m})$
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2013
%P 18-25
%V 6
%N 2
%U http://geodesic.mathdoc.fr/item/IIGUM_2013_6_2_a1/
%G ru
%F IIGUM_2013_6_2_a1
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/

[1] P. Hall, “A contribution to the theory of groups of prime-power order”, Proc. London Math. Soc., 36:1 (1934), 29–95 | DOI | MR

[2] M. Kholl, Teoriya grupp, Inostr. lit., M., 1962, 468 pp.

[3] V. D. Mazurov, E. I. Khukhro (red.), Kourovskaya tetrad. Nereshennye voprosy teorii grupp, 16-e izd., IM SO RAN, Novosibirsk, 2006, 180 pp.

[4] Yu. I. Merzlyakov, “Tsentralnye ryady i ryady kommutantov matrichnykh grupp”, Algebra i logika, 3:4 (1964), 49–58 | MR

[5] A. V. Yagzhev, “O regulyarnosti silovskikh $p$-podgrupp polnykh lineinykh grupp nad koltsami vychetov”, Mat. zametki, 56:6 (1994), 106–116 | MR | Zbl

[6] S. G. Kolesnikov, “O regulyarnosti silovskikh $p$-podgrupp grupp $GL_n(\mathbb{Z}_{p^m})$”, Issledovaniya po matematicheskomu analizu i algebre, v. 3, TGU, Tomsk, 2001, 117–124

[7] S. G. Kolesnikov, “O regulyarnykh silovskikh $p$-podgruppakh grupp Shevalle nad koltsom $\mathbb{Z}_{p^m}$”, Sib. mat. zhurn., 46:6 (2006), 1289–1295 | MR

[8] S. G. Kolesnikov, N. V. Maltsev, “O regulyarnosti silovskikh $p$-podgrupp simplekticheskikh i ortogonalnykh grupp nad koltsom $\mathbb{Z}_{p^m}$”, Zhurn. Sib. feder. un-ta. Matematika i fizika, 4:4 (2011), 489–497

[9] M. I. Kargapolov, Yu. I. Merzlyakov, Osnovy teorii grupp, Nauka, M., 1972, 240 pp. | MR | Zbl