The article deals with profinite groups in which centralizers are virtually procyclic. Suppose that G is a profinite group such that the centralizer of every nontrivial element is virtually torsion-free while the centralizer of every element of infinite order is virtually procyclic. We show that G is either virtually pro-p for some prime p or virtually torsion-free procyclic (Theorem 1.1). The same conclusion holds for profinite groups in which the centralizer of every nontrivial element is virtually procyclic (Theorem 1.2); moreover, if G is not pro-p, then G has finite rank.

中文翻译：

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中心化者实际上是顺周期的有界群

这篇文章讨论了其中的中心化器实际上是顺循环的profinite 组。假设G是一个超限群，使得每个非平凡元素的中心子实际上是无扭转的，而每个无限阶元素的中心子实际上是顺循环的。我们表明，摹或者是几乎亲p一些主要p或几乎无挠procyclic（定理1.1）。相同的结论适用于其中每个非平凡元素的中心化器实际上是顺循环的超限群（定理 1.2）；此外，如果G ^是不亲p，然后ģ具有有限秩。