论文标题
认识到$ a_6 \ times a_6 $ by共轭班级大小
On recognition of $A_6\times A_6$ by the set of conjugacy class sizes
论文作者
论文摘要
对于有限的组$ g $表示$ n（g）$ $ g $的共轭类尺寸。最近，提出了以下问题：如果每个非亚伯有限的简单组$ s $和每个$ n \ in \ mathbb {n} $中的每个$ n \，那么带有琐事中心的有限组$ g $的班级尺寸与直接Power $ s^n $的类班级尺寸相同，然后在本文中，我们通过证明$ a_6 \ times a_6 $由$ n（A_6 \ times a_6）$在具有微不足道的中心的有限组中唯一确定。
For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. Recently the following question has been asked: Is it true that for each nonabelian finite simple group $S$ and each $n\in\mathbb{N}$, if the set of class sizes of a finite group $G$ with trivial center is the same as the set of class sizes of the direct power $S^n$, then $G\simeq S^n$? In this paper we approach an answer to this question by proving that $A_6\times A_6$ is uniquely determined by $N(A_6\times A_6)$ among finite groups with trivial center.
