The Wielandt–Hartley theorem for submaximal X -subgroups

Standard

The Wielandt–Hartley theorem for submaximal X -subgroups. / Revin, Danila ; Skresanov, Saveliy ; Vasil’ev, Andrey.

In: Monatshefte fur Mathematik, Vol. 193, No. 1, 01.09.2020, p. 143-155.

Research output: Contribution to journal › Article › peer-review

Harvard

Revin, D , Skresanov, S & Vasil’ev, A 2020, 'The Wielandt–Hartley theorem for submaximal X -subgroups', Monatshefte fur Mathematik, vol. 193, no. 1, pp. 143-155. https://doi.org/10.1007/s00605-020-01425-4

APA

Revin, D., Skresanov, S., & Vasil’ev, A. (2020). The Wielandt–Hartley theorem for submaximal X -subgroups. Monatshefte fur Mathematik, 193(1), 143-155. https://doi.org/10.1007/s00605-020-01425-4

Vancouver

Revin D , Skresanov S , Vasil’ev A. The Wielandt–Hartley theorem for submaximal X -subgroups. Monatshefte fur Mathematik. 2020 Sept 1;193(1):143-155. doi: 10.1007/s00605-020-01425-4

Author

Revin, Danila ; Skresanov, Saveliy ; Vasil’ev, Andrey. / The Wielandt–Hartley theorem for submaximal X -subgroups. In: Monatshefte fur Mathematik. 2020 ; Vol. 193, No. 1. pp. 143-155.

BibTeX

@article{e74aa7d1415a46069a8791431a41d120,

title = "The Wielandt–Hartley theorem for submaximal X -subgroups",

abstract = "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.",

keywords = "Complete class, Finite nonsolvable group, Maximal X-subgroups, Submaximal X-subgroups, Subnormal subgroups",

author = "Danila Revin and Saveliy Skresanov and Andrey Vasil{\textquoteright}ev",

year = "2020",

month = sep,

day = "1",

doi = "10.1007/s00605-020-01425-4",

language = "English",

volume = "193",

pages = "143--155",

journal = "Monatshefte fur Mathematik",

issn = "0026-9255",

publisher = "Springer-Verlag GmbH and Co. KG",

number = "1",

}

RIS

TY - JOUR

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

AU - Revin, Danila

AU - Skresanov, Saveliy

AU - Vasil’ev, Andrey

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 -

ID: 24444620