Geodesic
Abnormality criteria for $p$-complements
Algebra i logika, Tome 55 (2016) no. 5, pp. 531-539.

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It is proved that for any finite group $G$ possessing a $p$-complement $H$ for some prime number $p$, the following assertions are equivalent: (1) all $p$-complements of $G$ are selfnormalizable; (2) all $p$-complements of $G$ are abnormal; (3) the subgroup $H$ is abnormal in $G$; (4) $NG(HX)=HX$ for any $X\trianglelefteq G$; (5) $G$ does not contain central chief pfactors.
Mots-clés : $p$-complement
Keywords: abnormal subgroup, pronormal subgroup, Hall subgroup. 
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E. P. Vdovin; D. O. Revin. Abnormality criteria for $p$-complements. Algebra i logika, Tome 55 (2016) no. 5, pp. 531-539. http://geodesic.mathdoc.fr/item/AL_2016_55_5_a0/

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