On the regularity Sylow's $p$-subgroups of symplectic and orthogonal groups over ring $\mathbb Z/p^m\mathbb Z$

Sergey G. Kolesnikov; Nikolay V. Maltsev

Geodesic

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On the regularity Sylow's $p$-subgroups of symplectic and orthogonal groups over ring $\mathbb Z/p^m\mathbb Z$

Sergey G. Kolesnikov ; Nikolay V. Maltsev

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 4, pp. 489-497

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Résumé

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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     title = {On the regularity {Sylow's} $p$-subgroups of symplectic and orthogonal groups over ring $\mathbb Z/p^m\mathbb Z$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {489--497},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2011_4_4_a6/}
}

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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/