CHARACTERIZING FINITE GROUPS WITH NORMAL -SUBGROUPS FOR THE SMALLEST PRIME DIVISOR OF THE ORDER OF THE GROUP

This article studies the group-theoretic constraints on particular subgroups of a finite group. These constraints are established through the concept of normality, resulting in a new group description. In particular, we consider a finite group with being the smallest prime divisor of its order. When every -subgroup is normal in , we say that is a -group. In the current paper, we provide a characterization of all finite -groups and show their main properties.