Algebra Seminar

It is of interesting to characterize the structure of a group G by the property of its subgroups in terms of normality. We call a subgroup M of G c-normal if it is suplemented by a normal subgroup N with the intersection of M and N in the core of M. We have proved that a finite group is solvable if and only if every maximal subgroup of G is c-normal. We will talk the motivation, the main properties and theorems about c-normal subgroups, applications and some recent generalizations about c-normality and related problems.