The number of conjugacy classes of non-normal subgroups in nilpotent groups

被引:25
作者
Poland, J [1 ]
Rhemtulla, A [1 ]
机构
[1] UNIV ALBERTA,DEPT MATH SCI,EDMONTON,AB T6G 2G1,CANADA
关键词
D O I
10.1080/00927879608825745
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In a recent paper, Rolf Brandl classified all finite groups having exactly one conjugacy class of nonnormal subgroups, and conjectured that for a nilpotent group G of nilpotency class c = c(G), the number v(G) = v of conjugacy classes of nonnormal subgroups satisfies the inequality v(G) greater than or equal to 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.
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页码:3237 / 3245
页数:9
相关论文
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