Geodesic
On non-periodic groups whose finitely generated subgroups are either permutable or pronormal
Mathematica Bohemica, Tome 138 (2013) no. 1, pp. 61-74.

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The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group $G$ is called a generalized radical, if $G$ has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the following\endgraf Theorem. Let $G$ be a locally generalized radical group whose finitely generated subgroups are either pronormal or permutable. If $G$ is non-periodic then every subgroup of $G$ is permutable.
DOI : 10.21136/MB.2013.143230
Classification : 20E07, 20E15, 20E25, 20E34, 20F14, 20F19, 20F22
Keywords: pronormal subgroup; permutable subgroup; finitely generated subgroup; abnormal subgroup 
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Kurdachenko, L. A.; Subbotin, I. Ya.; Ermolkevich, T. I. On non-periodic groups whose finitely generated subgroups are either permutable or pronormal. Mathematica Bohemica, Tome 138 (2013) no. 1, pp. 61-74. doi : 10.21136/MB.2013.143230. http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143230/

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