论文标题
许多元素具有主要电源顺序的小组
Profinite groups in which many elements have prime power order
论文作者
论文摘要
每个元素具有主要功率顺序（CP组）的有限和局部有限基团的结构是众所周知的。在本文中，我们注意到，我们较早的结果与有关有限CP组结构的可用信息的结合得出了与该属性的详细描述。然后，我们处理两种概括性CP组的概括。 定理1.2。对于某些prime P，当且仅当G中的每个非平地X中，prinite g组G组实际上是Pro-P，因此有一个prime P（取决于X），因此X的centralizer实际上是Pro-P。 定理1.3。令G为每个元素具有有限或质量功率（可能是无限）顺序的群体组。然后，对于某些prime p，g是扭转或实际上是pro-p。
The structure of finite and locally finite groups in which every element has prime power order (CP-groups) is well known. In this paper we note that the combination of our earlier results with the available information on the structure of finite CP-groups yields a detailed description of profinite groups with that property. Then we deal with two generalizations of profinite CP-groups. Theorem 1.2. A profinite group G is virtually pro-p for some prime p if and only if for each nontrivial x in G there is a prime p (depending on x) such that the centralizer of x is virtually pro-p. Theorem 1.3. Let G be a profinite group in which each element has either finite or prime power (possibly infinite) order. Then G is either torsion or virtually pro-p for some prime p.
