TY - JOUR

T1 - On pronormality and strong pronormality of Hall subgroups

AU - Nesterov, M. N.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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).

AB - 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).

KW - finite simple group

KW - Hall subgroup

KW - pronormal subgroup

KW - strongly pronormal subgroup

UR - http://www.scopus.com/inward/record.url?scp=85014645676&partnerID=8YFLogxK

U2 - 10.1134/S0037446617010165

DO - 10.1134/S0037446617010165

M3 - Article

AN - SCOPUS:85014645676

VL - 58

SP - 128

EP - 133

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 1

ER -