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On the Normal Subgroup with Exactly Two G-Conjugacy Class Sizes

【摘要】: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.

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