A note on finite groups with subnormal residuals of some sylow normalizers
EDN: JFHHSG
Abstract
Let $G$ be a group and the set of primes $\tau(G)=\cup\pi(G : M)$ for any maximal subgroup $M$ of $G$. For a non-empty nilpotent formation $\mathfrak{X}$, it is proved that a group $G$ has a nilpotent $\mathfrak{X}$-residual if and only if the $\mathfrak{X}$-residual of the $p$-Sylow normalizer is subnormal in $G$ for every $p$ from $\tau(G)$.
About the Authors
A. F. Vasil’ev
F. Scorina Gomel State University
Belarus
Belarus
Gomel
T. I. Vasil’eva
Belarusian State University of Transport
Belarus
Belarus
Gomel
A. G. Koranchuk
F. Scorina Gomel State University
Belarus
Belarus
Gomel
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Review
For citations:
Vasil’ev A.F., Vasil’eva T.I., Koranchuk A.G. A note on finite groups with subnormal residuals of some sylow normalizers. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2025;33(2):7-12. (In Russ.) EDN: JFHHSG
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