Abstract There has been some interest in understanding the relationship between the number of cyclic subgroups of a group and its order. This relationship is controlled in many cases by the size of the set of non-squares of the group. We improve upon previously established bounds and classify groups that obtain our new bound.

中文翻译：

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关于群的循环子群的个数

摘要 理解一个群的循环子群的数量与其阶数之间的关系引起了一些兴趣。在许多情况下，这种关系由组的非正方形集合的大小控制。我们改进先前建立的界限并对获得新界限的组进行分类。