On Finite Groups with -Subnormal Subgroups

• Published in: Mathematical Notes Vol. 114; no. 3-4; pp. 421 - 432
• Main Authors: Vasil’eva, T. I., Koranchuk, A. G.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 2023
• Subjects: 14/34; 639/766/189; 639/766/530; 639/766/747; Mathematics; Mathematics and Statistics; solvable group; subnormal subgroup; hereditary saturated formation; Sylow subgroup; supersolvable group
• ISSN: 0001-4346; 1573-8876
• DOI: 10.1134/S0001434623090158

Let
be a set of primes. A subgroup
of a group
is said to be
-subnormal in
if either
or there exists a chain of subgroups beginning with
and ending with
such that the index of each subgroup in the chain is either a prime in
or a
-number. Properties of
-subnormal subgroups are studied. In particular, it is proved that the class of all
-closed groups in which all Sylow subgroups are
-subnormal is a hereditary saturated formation. Criteria for the
-supersolvability of a
-closed group with given systems of
-subnormal subgroups are obtained.