Rocky Mountain Journal of Mathematics

On seminormal subgroups of finite groups

A. Ballester-Bolinches, J.C. Beidleman, V. Pérez-Calabuig, and M.F. Ragland

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Abstract

All groups considered in this paper are finite. A subgroup~$H$ of a group~$G$ is said to \textit {seminormal} in $G$ if $H$ is normalized by all subgroups~$K$ of~$G$ such that $\gcd (\lvert H\rvert , \lvert K\rvert )=1$. We call a group $G$ an MSN-\textit {group} if the maximal subgroups of all the Sylow subgroups of~$G$ are seminormal in~$G$. In this paper, we classify all MSN-groups.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 2 (2017), 419-427.

Dates
First available in Project Euclid: 18 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1492502543

Digital Object Identifier
doi:10.1216/RMJ-2017-47-2-419

Mathematical Reviews number (MathSciNet)
MR3635367

Zentralblatt MATH identifier
1380.20019

Subjects
Primary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks [See also 20F17]
Secondary: 20D15: Nilpotent groups, $p$-groups 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure

Keywords
Finite group soluble PST-group T$_0$-group MS-group MSN-group

Citation

Ballester-Bolinches, A.; Beidleman, J.C.; Pérez-Calabuig, V.; Ragland, M.F. On seminormal subgroups of finite groups. Rocky Mountain J. Math. 47 (2017), no. 2, 419--427. doi:10.1216/RMJ-2017-47-2-419. https://projecteuclid.org/euclid.rmjm/1492502543


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