The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.
A subgroup H of a group G is inert if |H: H ∩ H g| is finite for all g ∈ G and a group G is totally inert if every subgroup H of G is inert. We investigate the structure of minimal normal subgroups of totally inert groups and show that infinite locally graded simple groups cannot be totally inert.
This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained.
For a finite group and a non-linear irreducible complex character of write . In this paper, we study the finite non-solvable groups such that consists of at most two conjugacy classes for all but one of the non-linear irreducible characters of . In particular, we characterize a class of finite solvable groups which are closely related to the above-mentioned question and are called solvable -groups. As a corollary, we answer Research Problem in [Y. Berkovich and L. Kazarin: Finite...
On considère un immeuble de type ou , différents sous-ensembles de l’ensemble des sommets de et différents groupes d’automorphismes de , très fortement transitifs sur . On montre que l’algèbre des opérateurs -invariants agissant sur l’espace des fonctions sur est souvent non commutative (contrairement aux résultats classiques). Dans certains cas on décrit sa structure et on détermine ses fonctions radiales propres. On en déduit que la conjecture d’Helgason n’est pas toujours vérifiée...