Inequalities detecting structural properties of a finite group

被引：19

作者：

Garonzi, Martino ^{[1
]}

Patassini, Massimiliano ^{[1
]}

机构：

[1] Dipartimento Matemat Pura & Applicata, Padua, Italy

来源：

COMMUNICATIONS IN ALGEBRA | 2017年 / 45卷 / 02期

关键词：

Cyclic groups; Inequalities; Nilpotent groups; Order of an element; ORDERS;

D O I：

10.1080/00927872.2016.1172621

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove several results detecting cyclicity or nilpotency of a finite group G in terms of inequalities involving the orders of the elements of G and the orders of the elements of the cyclic group of order |G|. We prove that, among the groups of the same order, the number of cyclic subgroups is minimal for the cyclic group, and the product of the orders of the elements is maximal for the cyclic group.

引用

页码：677 / 687

页数：11

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