Geodesic
On transitivity of pronormality
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 4, pp. 583-594.

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This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained.
Classification : 20E15, 20F16
Keywords: pronormal subgroups; transitive relations 
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Kurdachenko, Leonid A.; Subbotin, Igor Ya. On transitivity of pronormality. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 4, pp. 583-594. http://geodesic.mathdoc.fr/item/CMUC_2002__43_4_a0/