TY - JOUR

T1 - The Wielandt–Hartley theorem for submaximal X -subgroups

AU - Revin, Danila

AU - Skresanov, Saveliy

AU - Vasil’ev, Andrey

N1 - Publisher Copyright: © 2020, Springer-Verlag GmbH Austria, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - A nonempty class X of finite groups is called complete if it is closed under taking subgroups, homomorphic images and extensions. We consider two definitions of submaximal X-subgroups suggested by H. Wielandt and discuss which one better suits the task of determining maximal X-subgroups. We prove that these definitions are not equivalent yet the Wielandt–Hartley theorem holds true for either definition of X-submaximality. We also give some applications of the strong version of the Wielandt–Hartley theorem.

AB - A nonempty class X of finite groups is called complete if it is closed under taking subgroups, homomorphic images and extensions. We consider two definitions of submaximal X-subgroups suggested by H. Wielandt and discuss which one better suits the task of determining maximal X-subgroups. We prove that these definitions are not equivalent yet the Wielandt–Hartley theorem holds true for either definition of X-submaximality. We also give some applications of the strong version of the Wielandt–Hartley theorem.

KW - Complete class

KW - Finite nonsolvable group

KW - Maximal X-subgroups

KW - Submaximal X-subgroups

KW - Subnormal subgroups

UR - http://www.scopus.com/inward/record.url?scp=85086025347&partnerID=8YFLogxK

U2 - 10.1007/s00605-020-01425-4

DO - 10.1007/s00605-020-01425-4

M3 - Article

AN - SCOPUS:85086025347

VL - 193

SP - 143

EP - 155

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 1

ER -