Geodesic
Abnormal subgroups and Carter subgroups in some infinite groups
Algebra and discrete mathematics, no. 1 (2005), pp. 69-83.

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Some properties of abnormal subgroups in generalized soluble groups are considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it is proven that a subgroup H of a radical group G is abnormal in G if and only if every intermediate subgroup for H coincides with its normalizer in G. This result extends on radical groups the well-known criterion of abnormality for finite soluble groups due to D. Taunt. For some infinite groups (not only periodic) the existence of Carter subgroups and their conjugation have been also obtained.
Mots-clés : abnormal subgroups, pronormal subgroups, Carter subgroups. 
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     author = {L. A. Kurdachenko and I. Ya. Subbotin},
     title = {Abnormal subgroups and {Carter} subgroups in some infinite groups},
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L. A. Kurdachenko; I. Ya. Subbotin. Abnormal subgroups and Carter subgroups in some infinite groups. Algebra and discrete mathematics, no. 1 (2005), pp. 69-83. https://geodesic-test.mathdoc.fr/item/ADM_2005_1_a6/