This article is cited in 4 papers

On pronormality and strong pronormality of Hall subgroups

M. N. Nesterov<sup>ab

a</sup> Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: We study several well-known questions on pronormality and strong pronormality of Hall subgroups. In particular, we exhibit the examples of finite groups (a) having a Hall subgroup not pronormal in its normal closure (this solves Problem 18.32 of The Kourovka Notebook in the negative); (b) having a Hall subgroup pronormal but not strongly pronormal; and (c) that are simple, having a Hall subgroup, and not strongly pronormal (this solves Problem 17.45(b) of The Kourovka Notebook in the negative).

Keywords: Hall subgroup, pronormal subgroup, strongly pronormal subgroup, finite simple group.

UDC: 512.542

MSC: 35R30

Received: 03.03.2016

DOI: 10.17377/smzh.2017.58.116

 English version: Siberian Mathematical Journal, 2017, 58:1, 128–133

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