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

详细信息    查看全文

• 作者：Lili Li^a ; Haipeng Qu^b ; ^{orcawhle@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：20D15
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：466
• 期：Complete
• 页码：44-62
• 全文大小：395 K

文摘

Assume k is a positive integer and p   is a prime. Let ν(G)$\nu (G)$ be the number of conjugacy classes of nonnormal subgroups of a finite group G   and N_CN(p,k)={ν(G)∈[0,kp]|G is a finite p-group}${\mathcal{N}}_{CN}(p,k)=\{\nu (G)\in [0,kp]|G\text{is a finite}p\text{-group}\}$. In this paper, the set N_CN(p,k)${\mathcal{N}}_{CN}(p,k)$ is determined for k≤2$k\le 2$, and it is discovered that there is a new gap in the values that ν(G)$\nu (G)$ can take in the case of finite p-groups. In particular, the number of conjugacy classes of nonnormal subgroups of minimal non-abelian p-groups is determined.