Geodesic
One necessary condition for the regularity of a $p$-group and its application to Wehrfritz's problem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 138-163

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We obtain a necessary condition for the regularity of a $p$-group in terms of segments of P. Hall's collection formula. For any prime number $p$ such that $(p+2)/3$ is an integer, we prove that a Sylow $p$-subgroup of the group $GL_n(\mathbb{Z}_{p ^ m})$ is not regular if $n \geqslant (p+2)/3$ and $m \geqslant 3.$ We also list all regular Sylow $p$-subgroups of the Chevalley group of type $G_2$ over the ring $\mathbb{Z}_{p^m}.$
Keywords: regular $p$-group, linear group, Chevalley group. 
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     title = {One necessary condition for the regularity of a $p$-group and its application to {Wehrfritz's} problem},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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S. G. Kolesnikov; V. M. Leontiev. One necessary condition for the regularity of a $p$-group and its application to Wehrfritz's problem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 138-163. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a6/