Geodesic
On $\pi$-solvability of a finite group with a partially permutable $\pi$-Hall subgroup
Problemy fiziki, matematiki i tehniki, no. 1 (2010), pp. 25-27

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We investigate a finite group such that its $\pi$-Hall subgroup is permutable with some subgroups of the group. For instance, we establish $\pi$-solvability of such groups in two cases: a $\pi$-Hall subgroup is 2-nilpotent; a $\pi$-Hall subgroup is solvable and $3\notin\pi$. Besides, we establish solvability of a finite group in the case when a 2-nilpotent $\pi$-Hall subgroup of the group has odd index.
Keywords: finite group, seminormal subgroup, $\pi$-Hall subgroup
Mots-clés : $\pi$-solvable group. 
@article{PFMT_2010_1_a4,
     author = {V. N. Kniahina},
     title = {On $\pi$-solvability of a finite group with a partially permutable $\pi${-Hall} subgroup},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {25--27},
     publisher = {mathdoc},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2010_1_a4/}
}
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V. N. Kniahina. On $\pi$-solvability of a finite group with a partially permutable $\pi$-Hall subgroup. Problemy fiziki, matematiki i tehniki, no. 1 (2010), pp. 25-27. http://geodesic.mathdoc.fr/item/PFMT_2010_1_a4/