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| On the Normal Subgroup with Exactly Two G-Conjugacy Class Sizes |
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Citation： |
Xianhe ZHAO,Xiuyun GUO.On the Normal Subgroup with Exactly Two G-Conjugacy Class Sizes[J].Chinese Annals of Mathematics B,2009,30(4):427~432 |
| Page view： 1845
Net amount： 1439 |
Authors： |
Xianhe ZHAO; Xiuyun GUO; |
Foundation： |
the National Natural Science Foundation of China (No. 10771132), SGRC (No.
GZ 310), the Research Grant of Shanghai University and the Shanghai Leading Academic Discipline
Project (No. J50101). |
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| Abstract： |
Let G be a finite group with a non-central Sylow r-subgroup R, Z(G) the
center of G, and N a normal subgroup of G. The purpose of this paper is to determine
the structure of N under the hypotheses that N contains R and the G-conjugacy class
size of every element of N is either 1 or m. Particularly, it is shown that N is Abelian if
N \ Z(G) = 1 and the G-conjugacy class size of every element of N is either 1 or m. |
Keywords： |
Normal subgroups, Conjugacy class sizes, Nilpotent groups |
Classification： |
20D10, 20D20 |
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