Criteria for $\pi$-separability of a finite group
Problemy fiziki, matematiki i tehniki, no. 4 (2021), pp. 81-84
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Throughout this paper all groups are finite and $G$ always denotes a finite group. The group $G$ is said to be $\pi$-separable if every chief factor of $G$ is either a $\pi$-group or a $\pi'$-group. A subgroup $A$ of $G$ is said to be $\pi,\pi'$-subnormal in $G$ if there is a subgroup chain $A=A_0\leqslant A_1\leqslant\dots\leqslant A_n=G$ such that either $A_{i-1}\trianglelefteq A_i$ or $A_i/(A_{i-1})_{A_i}$ is a $\pi$-separable group for all $i = 1, \dots, n$. In this paper we study the influence of $\pi,\pi'$-subnormal subgroups on the structure of the group.
Keywords:
finite group, $\pi$-separable group, $\pi,\pi'$-subnormal subgroup, Hall subgroup.
@article{PFMT_2021_4_a12,
author = {I. M. Dergacheva and I. P. Shabalina and E. A. Zadorozhnyuk},
title = {Criteria for $\pi$-separability of a finite group},
journal = {Problemy fiziki, matematiki i tehniki},
pages = {81--84},
year = {2021},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/PFMT_2021_4_a12/}
}
I. M. Dergacheva; I. P. Shabalina; E. A. Zadorozhnyuk. Criteria for $\pi$-separability of a finite group. Problemy fiziki, matematiki i tehniki, no. 4 (2021), pp. 81-84. http://geodesic.mathdoc.fr/item/PFMT_2021_4_a12/
[1] O.H. Kegel, “Untergruppenverbande endlicher Gruppen, die den subnormalteilerverband echt enthalten”, Arch. Math., 30:3 (1978), 225–228 | DOI | MR | Zbl
[2] D. Gorenstein, Finite Groups, Harper Row Publishers, New York–Evanston–London, 1968
[3] B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin–Heidelberg–New York, 1967
[4] L.A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978