Abstract

The same-order type τ_e(G) of a finite group G is a set formed of the sizes of the equivalence classes containing the same order elements of G. In this paper, we study an arithmetical property of this set. More exactly, we outline some results on the classification and existence of finite groups whose same-order types are arithmetic progressions formed of 3 or 4 elements, the latter being the maximum size of such a sequence.

中文翻译：

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同阶类型为算术级数的群

摘要

有限群G的同阶类型τ _e ( G ) 是由包含G的同阶元素的等价类的大小组成的集合。在本文中，我们研究了这个集合的算术性质。更准确地说，我们概述了有限群的分类和存在的一些结果，这些有限群的同阶类型是由 3 个或 4 个元素组成的算术级数，后者是这种序列的最大大小。