On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups

Standard

On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups. / Guo, W.; Maslova, N. V.; Revin, D. O.

In: Siberian Mathematical Journal, Vol. 59, No. 4, 01.07.2018, p. 610-622.

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

Harvard

Guo, W, Maslova, NV & Revin, DO 2018, 'On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups', Siberian Mathematical Journal, vol. 59, no. 4, pp. 610-622. https://doi.org/10.1134/S0037446618040043

APA

Guo, W., Maslova, N. V., & Revin, D. O. (2018). On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups. Siberian Mathematical Journal, 59(4), 610-622. https://doi.org/10.1134/S0037446618040043

Vancouver

Guo W, Maslova NV, Revin DO. On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups. Siberian Mathematical Journal. 2018 Jul 1;59(4):610-622. doi: 10.1134/S0037446618040043

Author

Guo, W. ; Maslova, N. V. ; Revin, D. O. / On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups. In: Siberian Mathematical Journal. 2018 ; Vol. 59, No. 4. pp. 610-622.

BibTeX

@article{f20b14c227494302a1f6c5c60636737c,

title = "On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups",

abstract = "We study finite groups with the following property (*): All subgroups of odd index are pronormal. Suppose that G has a normal subgroup A with property (*), and the Sylow 2-subgroups of G/A are self-normalizing. We prove that G has property (*) if and only if so does NG(T)/T, where T is a Sylow 2-subgroup of A. This leads to a few results that can be used for the classification of finite simple groups with property (*).",

keywords = "direct product, finite group, pronormal subgroup, self-normalizing subgroup, simple group, subgroup of odd index, Sylow 2-subgroup, symplectic group, wreath product",

author = "W. Guo and Maslova, {N. V.} and Revin, {D. O.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = jul,

day = "1",

doi = "10.1134/S0037446618040043",

language = "English",

volume = "59",

pages = "610--622",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "4",

}

RIS

TY - JOUR

T1 - On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups

AU - Guo, W.

AU - Maslova, N. V.

AU - Revin, D. O.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - We study finite groups with the following property (*): All subgroups of odd index are pronormal. Suppose that G has a normal subgroup A with property (*), and the Sylow 2-subgroups of G/A are self-normalizing. We prove that G has property (*) if and only if so does NG(T)/T, where T is a Sylow 2-subgroup of A. This leads to a few results that can be used for the classification of finite simple groups with property (*).

AB - We study finite groups with the following property (*): All subgroups of odd index are pronormal. Suppose that G has a normal subgroup A with property (*), and the Sylow 2-subgroups of G/A are self-normalizing. We prove that G has property (*) if and only if so does NG(T)/T, where T is a Sylow 2-subgroup of A. This leads to a few results that can be used for the classification of finite simple groups with property (*).

KW - direct product

KW - finite group

KW - pronormal subgroup

KW - self-normalizing subgroup

KW - simple group

KW - subgroup of odd index

KW - Sylow 2-subgroup

KW - symplectic group

KW - wreath product

UR - http://www.scopus.com/inward/record.url?scp=85053003395&partnerID=8YFLogxK

U2 - 10.1134/S0037446618040043

DO - 10.1134/S0037446618040043

M3 - Article

AN - SCOPUS:85053003395

VL - 59

SP - 610

EP - 622

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -

ID: 16485716