Finite groups with generalized subnormal embedding of Sylow subgroups

• Published in: Siberian mathematical journal Vol. 57; no. 2; pp. 200 - 212
• Main Authors: Vasil’ev, A. F., Vasil’eva, T. I., Vegera, A. S.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-03-2016
• Subjects: Mathematics; Mathematics and Statistics; finite group; subnormal subgroup; hereditary saturated formation; formation; K; local screen; Sylow subgroup
• ISSN: 0037-4466; 1573-9260
• DOI: 10.1134/S0037446616020038

Given a set
π
of primes and a hereditary saturated formation
F
, we study the properties of the class of groups
G
for which the identity subgroup and all Sylow
p
-subgroups are
F
-subnormal (K-
F
-subnormal) in
G
for each
p
in
π
. We show that such a class is a hereditary saturated formation and find its maximal inner local screen. Some criteria are obtained for the membership of a group in a hereditary saturated formation in terms of its formation subnormal Sylow subgroups.