Isomorphisms between lattices of almost normal subgroups

A subgroupH of a groupG is said to bealmost normal inG if it has only finitely many conjugates inG. The setan(G) of almost normal subgroups ofG is a sublattice of the lattice of all subgroups ofG. Isomorphisms between lattices of almost normal subgroups ofFC-soluble groups are considered in this paper. In particular, properties of images of normal subgroups under such an isomorphism are investigated.     

Automorphisms and normal subgroups of linear groups

In the present paper, the properties of orders of coprime automorphisms of irreducible linear groups are established and sufficient conditions for the existence of a normal Hall π-subgroup in a given π-separable irreducible complex linear group are obtained. Библиография: 11 наэваний.     

Injectors and normal subgroups of finite groups

A class of subgroups,N-injectors, previously defined only for soluble groups, is here defined for some non-soluble groups. It is proved that injectors have some properties which resemble those of Sylow subgroups.     

Weakly normal subgroups of finite groups

A subgroup H of a group G is weakly normal in G if H ^g ≤ N _G (H) implies that g ∈ N _G (H). In this paper, we shall obtain some characterizations about the supersolvability and nilpotency of G by assuming that some subgroups of prime power order of G are weakly normal in G.     

Pro-p groups with few normal subgroups

Motivated by the study of pro-p groups with finite coclass, we consider the class of pro-p groups with few normal subgroups. This is not a well defined class and we offer several different definitions and study the connections between them. Furthermore, we propose a definition of periodicity for pro-p groups, thus, providing a general framework for some periodic patterns that have already been observed in the existing literature. We then focus on examples and show that strikingly all the interesting examples not only have few normal subgroups, but in addition have periodicity in the lattice of normal subgroups.