Generalised norms in finite soluble groups

The number of conjugacy classes of nonnormal subgroups of finite p-groups

G, we dene the subgroup A(G) to be intersection of the normalizers of all non-cyclic subgroups of G. Set A0 = 1. Dene Ai+1(G)=Ai(G) = A(G=Ai(G)) for i 1. By A1 (G) denote the terminal term of the ascending series. It is proved that if G.

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Finite non-nilpotent generalizations of hamiltonian groups

A group is called metahamiltonian if all non-abelian subgroups of it are normal. This concept is a natural generation of Hamiltonian groups. In this paper, a complete classification of finite metahamiltonian $p$-groups is given.

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The Classification of Finite Metahamiltonian $p$-Groups

In this paper, we classify finite 2-groups all of whose nonnormal subgroups have orders at most 23. Together with a known result, we completely solved Problem 2279 proposed by Y. Berkovich and Z. Janko in Groups of Prime Power Order, Vol. 3.

Haipeng Qu

Papers

Finite groups which have many normal subgroups