Abstract
A subgroup H of a group G is called nearly pronormal in G if, for every subgroup L of the group G that contains H, the normalizer N L (H) is contranormal in L. We prove that if G is a (generalized) solvable group in which every subgroup is nearly pronormal, then all subgroups of G are pronormal.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1331–1338, October, 2007.
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Vincenzi, G., Kurdachenko, L.A. & Russo, A. On some groups all subgroups of which are nearly pronormal. Ukr Math J 59, 1493–1500 (2007). https://doi.org/10.1007/s11253-008-0007-x
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DOI: https://doi.org/10.1007/s11253-008-0007-x