%0 Journal Article
%T 素数幂、双素数幂阶元的共轭类长的个数为4的 有限群的结构<br>Structure of Finite Groups with Four Conjugacy Class Sizes of Primary and Biprimary Elements
%A 邵长国
%A 蒋琴会
%J 数学年刊（A辑）
%D 2018
%R 10.16205/j.cnki.cama.2018.0001
%X 设群$G$为一个有限群. 如果群$G$中素数幂、双素幂阶元的共轭类长的集合为$\{1,p^a,m,p^bm\}$, 那么群$G$是可解的, 其中$a>b$为正整数, $p$为素数且与$m$互素. 进一步, 给出了群$G/\textbf{Z}(G)$的结构, 这是对文``Chen R F, Zhao X H. A criterion for a group to have nilpotent $p$-complements [J]. {\it Monatsh Math}, 2016, 179(2):221--225''中定理A主要结论的一个推广.<br>Let $G$ be a finite group. It is proved that $G$ is solvable if the set of its conjugacy class sizes of primary and biprimary elements is $\{1, p^a, m, p^bm\}$, where $a > b$ are two positive integers and $p$ is a prime coprime to integer $m$. Moreover, the authors give a detailed structure description of $G/\textbf{Z}(G)$, which generalizes the main result of Theorem A in ``Chen, R. F. and Zhao, X. H., {\it Monatsh. Math.}, 2016, 179(2):221--225''.
%K 有限群
%K 素数幂、双素幂阶元
%K 共轭类长
%K 2-Frobenius群&lt
%K br&gt
%K Finite groups
%K Primary and biprimary elements
%K Conjugacy class sizes
%K 2-Frobenius groups
%U http://www.camath.fudan.edu.cn/camacn/ch/reader/view_abstract.aspx?file_no=39A101&flag=1