论文标题
共轭类的正方形和Baer-Suzuki定理的变体
Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem
论文作者
论文摘要
对于$ p $ a Prime，$ g $一个有限的组和$ a $ a订单$ p $元素的一个正常子集，我们证明，如果$ a^2 = \ {ab \ \ \ \ \ \ \ \ \ \ \ \ \ him a，b \ in a \} $中的$ p $ elements，则$ q = \ langle a \ rangle a \ rangle $ soluble。此外，如果$ o_p（g）= 1 $，我们表明$ p $是奇数，$ f（q）$是一个非平凡的$ p'$ - 组，$ q/f（q）$是小学的Abelian $ p $ -group。我们还提供了表明该结论最好的例子。
For $p$ a prime, $G$ a finite group and $A$ a normal subset of elements of order $p$, we prove that if $A^2 = \{ab \mid a, b \in A\}$ consists of $p$-elements then $Q = \langle A \rangle$ is soluble. Further, if $O_p(G) = 1$, we show that $p$ is odd, $F(Q)$ is a non-trivial $p'$-group and $Q/F(Q)$ is an elementary abelian $p$-group. We also provide examples which show this conclusion is best possible.
