On the regularity Sylow's $p$-subgroups of symplectic and orthogonal groups over ring $\mathbb Z/p^m\mathbb Z$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 4, pp. 489-497.

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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, Sylow subgroup.
Mots-clés : orthogonal group
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Sergey G. Kolesnikov; Nikolay V. Maltsev. On the regularity Sylow's $p$-subgroups of symplectic and orthogonal groups over ring $\mathbb Z/p^m\mathbb Z$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 4, pp. 489-497. http://geodesic.mathdoc.fr/item/JSFU_2011_4_4_a6/

[1] P. Hall, “A conribution to the theory of groups of prime-power order”, Proc. London Math. Soc., s2-36:1 (1934), 29–95 | DOI

[2] M. Kholl, Teoriya grupp, IL, M., 1962

[3] Mazurov V. D., Khukhro E. I. (red.), Kourovskaya tetrad. Nereshennye voprosy teorii grupp, 16-e izdanie, 2006 http://www.math.nsc.ru

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

[5] S. G. Kolesnikov, “O regulyarnosti silovskikh $p$-podgrupp grupp $GL_n(\mathbb Z_{p^m})$”, Issl. po matem. analizu i algebre, 3 (2001), 117–124

[6] S. G. Kolesnikov, “O regulyarnykh silovskikh $p$-podgruppakh grupp Shevalle nad koltsom $\mathbb Z_{p^m}$”, Sib. matem. zhurnal, 47:6 (2006), 1289–1295 | MR | Zbl

[7] M. I. Kargapolov, Yu. I. Merzlyakov, Osnovy teorii grupp, Nauka, M., 1977 | MR | Zbl

[8] Yu. V. Sosnovskii, “Kommutatornoe stroenie simplekticheskikh grupp”, Matem. zametki, 24:5 (1978), 641–648 | MR | Zbl

[9] Yu. V. Sosnovskii, Kommutatornoe stroenie i izomorfizmy klassicheskikh grupp, Dissertatsiya na soiskanie uch. step. k.f.-m.n., Novosibirsk, 1980

[10] V. M. Levchuk, “Kommutatornoe stroenie nekotorykh podgrupp grupp Shevalle”, Ukr. mat. zhurnal, 44:6 (1992), 786–795 | MR | Zbl