The number of conjugacy classes of non-normal subgroups in nilpotent groups
The number of conjugacy classes of non-normal subgroups in nilpotent groups
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DOI：
10.1080/00927879608825745
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发表时间：
1996
影响因子：
0.7
通讯作者：
John Poland;A. Rhemtulla
中科院分区：
文献类型：
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作者：
John Poland;A. Rhemtulla
Rolf Brandi在最近的一篇文章中对所有具有一个共轭类的有限群进行了分类，并证明了对于幂零类c = c（G）的幂零群G，非正规子群的共轭类的个数v（G）= v满足不等式v（G）≥ c（G）- 1（当然，Hamilton群除外）.本文的目的是建立这一猜想，并决定何时这个不等式是尖锐的。
In a recent paper, Rolf Brandi classified all finite groups having exactly one conjugacy class of nonnormal subgroups, and conjectured thatfor a nilpotent group G of nilpotency class c = c(G) the number v(G) = vof conjugacy classes of nonnormal subgroups satisfies the inequality v(G) ≥ c(G) – 1 (with the exception of the Hamiltonian groups, of course). The purpose of this paper is to establish this conjecture and to decide when this inequality is sharp.