تفاصيل الرسالة العلمية

This thesis delves into normal 2-groups, finite groups where every 2-subgroup is normal. It characterizes these groups, excluding odd-order cases, drawing inspiration from Dedekind and Hamiltonian groups. Core findings classify normal 2-groups into abelian groups, direct products with the quaternion group, elementary abelian 2-groups, and certain abelian groups of odd order. The study explores their solvability within finite solvable groups. Illustrative examples demonstrate diversity, including cases where they aren't nilpotent or supersolvable. The thesis contributes insights into the closure properties of normal 2-groups. In conclusion, it outlines open questions and suggests future research directions in the realm of normal 2-groups, providing a comprehensive exploration of their classification and structural properties