The structure of locally soluble groups in which all subgroups are pronormal is known, and
many authors have investigated groups which are rich in pronormal subgroups. Here we …

A group is called HNN-free if it has no subgroups that are nontrivial HNN-extensions. We
prove that finitely generated HNN-free implies virtually polycyclic for a large class of groups …

arXiv:2307.09003v1 [math.GR] 18 Jul 2023 Groups with the real chain condition on non-pronormal
subgroups Page 1 arXiv:2307.09003v1 [math.GR] 18 Jul 2023 Groups with the real chain …

Some influential families of subgroups such as pronormal subgroups, contranormal
subgroups, and abnormal subgroups, their generalizations, characterizations, interplays …

We extend some results known for FC-groups to the class FC* of generalized FC-groups
introduced in de Giovanni et al.['Groups with restricted conjugacy classes', Serdica Math. J …

In recent times, group theory has found wider applications in various fields of algebra and
mathematics in general. But in order to apply this or that result, you need to know about it …

A subgroup H of a group G is said to be weakly normal if H g= H whenever g is an element
of G such that H g≤ NG (H). There is a strictly relation between weak normality and groups …

We study groups in which normality is a weakly transitive relation, giving an extension of in
Theorem A [On finite T-groups, J. Aust. Math. Soc. 75 (2003) 181–191] due to Ballester …

A subgroup $ X $ of‎‎ a group $ G $ is said to be an H-‎ subgroup if‎‎ NG (X)∩ Xg≤ X for each
element $ g $ belonging to $ G $‎.‎ In [M‎.‎ Bianchi and ea‎,‎ On finite soluble groups in which …

The survey is dedicated to investigation of groups with prescribed properties of generalized
normal subgroups. The roots of such investigations lie in the works by R. Dedekind, R. Baer …