Let G be a finite p-group. Assume that \(\nu (G)\) and \(\nu _c(G)\) denote the number of conjugacy classes of non-normal subgroups and non-normal cyclic subgroups of G, respectively. In this paper, we completely classify the finite p-groups with \(\nu _c=p\) or \(p+1\) for an odd prime number p. Also, we classify the groups G with \(\nu (G)=\nu _c(G)=p^i, i\ge 1\).

中文翻译：

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关于循环非正规子群的共轭类

令G为有限的p-群。假设\（\ NU（G）\）和\（\ NU _c（G）\）表示非正常子群和非正常循环子群的共轭类的数量ģ，分别。在本文中，对于奇质数p，我们用\（\ nu _c = p \）或\（p + 1 \）对有限的p-组进行了完全分类。同样，我们用\（\ nu（G）= \ nu _c（G）= p ^ i，i \ ge 1 \）对组G进行分类。