A Note on the Structure of Groups of Order 2~np~2(n≥3)
LI Quan-na
Abstract
LI Quan-na
Abstract
In this paper,by using the special structures of some groups which are dihedral groups,or semi-dihedral groups,or quaternion groups,and some theorems in extension of groups,we obtain the classification of groups of order 2np2,Sylow p-subgroups of which are self-normalizer,and Sylow 2-subgroups are dihedral or semi-dihedral or quaternion groups.
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In this paper,by using the special structures of some groups which are dihedral groups,or semi-dihedral groups,or quaternion groups,and some theorems in extension of groups,we obtain the classification of groups of order 2np2,Sylow p-subgroups of which are self-normalizer,and Sylow 2-subgroups are dihedral or semi-dihedral or quaternion groups.
Key concepts: Sylow theorems, Dihedral group, Dihedral angle, Mathematics, Centralizer and normalizer, Quaternion, Order (exchange), Group (periodic table)