Finite $$p$$ p -Groups all of Whose Nonnormal Subgroups Posses Special Normalizers

Abstract

In this paper, finite \(p\)-groups \(G\) with \(N_G(H)/H\) being cyclic for all nonnormal subgroups \(H\) are classified up to isomorphism. As a by-product, finite \(p\)-groups all of whose nonnormal subgroup are uniserially embedded subgroups are classified. We solved tow problems introduced by Y. Berkovich.