Geodesic
Pronormality and strong pronormality of subgroups
Algebra i logika, Tome 52 (2013) no. 1, pp. 22-33.

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A subgroup $H$ of a group $G$ is said to be pronormal if, for any element $g\in G$, subgroups $H$ and $H^g$ are conjugate in $\langle H,H^g\rangle$. A subgroup $H$ of a group $G$ is said to be strongly pronormal if, for any subgroup $K\le H$ and any element $g\in G$, there exists an element $x\in\langle H,K^g\rangle$ such that $K^{gx}\le H$. Many known examples of pronormal subgroups, namely, normal subgroups, maximal subgroups, Sylow subgroups of finite groups, and Hall subgroups of finite soluble groups, will also exemplify strongly pronormal subgroups. It is shown that Carter subgroups of finite groups (which are always pronormal) are not strongly pronormal in general, even in soluble groups.
Mots-clés : pronormal group
Keywords: strongly pronormal group, Carter subgroup, finite group. 
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E. P. Vdovin; D. O. Revin. Pronormality and strong pronormality of subgroups. Algebra i logika, Tome 52 (2013) no. 1, pp. 22-33. http://geodesic.mathdoc.fr/item/AL_2013_52_1_a1/

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