论文标题
Neumann的BFC Theorem的一种更强的形式
A stronger form of Neumann's BFC-theorem
论文作者
论文摘要
给定一个$ g $，我们为包含元素$ x $的$ g $的共轭类写$ x^g $。 B. H. Neumann的著名定理指出，如果$ g $是所有共轭类都是有限尺寸的团体，那么派生的$ g'$是有限的。我们建立以下结果。 令$ n $为一个正整数，$ k $一个组$ g $的子组，以便$ | x^g | \ leq n $对于k $中的每个$ x \。令$ h = \ langle k^g \ rangle $为$ k $的正常关闭。然后，派生的组$ h'$的顺序是有限的，$ n $结合了。 还讨论了该结果的一些推论。
Given a group $G$, we write $x^G$ for the conjugacy class of $G$ containing the element $x$. A famous theorem of B. H. Neumann states that if $G$ is a group in which all conjugacy classes are finite with bounded size, then the derived group $G'$ is finite. We establish the following result. Let $n$ be a positive integer and $K$ a subgroup of a group $G$ such that $|x^G|\leq n$ for each $x\in K$. Let $H=\langle K^G\rangle$ be the normal closure of $K$. Then the order of the derived group $H'$ is finite and $n$-bounded. Some corollaries of this result are also discussed.
