Abnormal subgroups and Carter subgroups in some infinite groups - Kurdachenko, L.A.; Subbotin, I.Ya. (Algebra and Discrete Mathematics, 2005)
t. 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 wellknown 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.