Cyclicity degrees of finite groups

被引：13

作者：

Tarnauceanu, M. ^{[1
]}

Toth, L. ^{[2
]}

机构：

[1] Alexandru Ioan Cuza Univ, Fac Math, Iasi, Romania

[2] Univ Pecs, Dept Math, Pecs, Hungary

来源：

ACTA MATHEMATICA HUNGARICA | 2015年 / 145卷 / 02期

关键词：

cyclicity degree; subgroup lattice; poset of cyclic subgroups; number of subgroups; SUBGROUP COMMUTATIVITY DEGREES; PROBABILITY; ELEMENTS;

D O I：

10.1007/s10474-015-0480-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce and study the concept of cyclicity degree of a finite group G. This quantity measures the probability of a random subgroup of G to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An asymptotic formula and minimality/maximality results on cyclicity degrees are also inferred.

引用

页码：489 / 504

页数：16

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