Abstract.
A subgroup H of G is said to be $\pi$-quasinormal in G if it permute with every Sylow subgroup of G. In this paper, we extend the study on the structure of a finite group under the assumption that some subgroups of G are $\pi$-quasinormal in G. The main result we proved in this paper is the following:
Theorem 3.4. Let ${\cal F}$ be a saturated formation containing the supersolvable groups. Suppose that G is a group with a normal subgroup H such that $G/H \in {\cal F}$, and all maximal subgroups of any Sylow subgroup of $F^{*}(H)$ are $\pi$-quasinormal in G, then $G \in {\cal F}$.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding authors
Additional information
Received: 10 May 2002
Rights and permissions
About this article
Cite this article
Li, Y., Wang, Y. & Wei, H. The influence of $\pi$-quasinormality of some subgroups of a finite group. Arch. Math. 81, 245–252 (2003). https://doi.org/10.1007/s00013-003-0829-6
Issue Date:
DOI: https://doi.org/10.1007/s00013-003-0829-6