在這篇論文中，我們列出一些與元素的指數(index)相關的結果。首先是和指數為質數次方的元素有關的結果，包含單一性(simplicity)，normal p-complement 的存在性，以及一個元素擁有質數次方的指數的充分條件。接著我們舉一些例子說明滿足 order 為質數次方的元素都有質數次方指數這種條件的群還有 q-Baer 群。最後列出由元素的指數所推導出的和群的可解性(solubility)有關的結果。

In this thesis, we show some results about index of an element. We first show results about elements of prime-power indices, which include simplicity, the existence of normal p-complements, and sufficient conditions for an element to have prime-power index. Next, we give some examples of groups such that elements of prime-power order have prime-power indices, and q-Baer groups. The last part, we show some results that the indices of elements in a group can imply the solubility of it.

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