Harmonic numbers and finite groups

被引：3

作者：

Baishya, Sekhar Jyoti ^{[1
]}

Das, Ashish Kumar ^{[1
]}

机构：

[1] NE Hill Univ, Dept Math, Shillong 793022, Meghalaya, India

来源：

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA | 2014年 / 132卷

关键词：

Finite groups; harmonic numbers; harmonic groups; POSITIVE DIVISORS; INEQUALITY; ORDERS;

D O I：

10.4171/RSMUP/132-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a finite group G, let tau(G) be the number of normal subgroups of G and sigma(G) be the sum of the orders of the normal subgroups of G. The group G is said to be harmonic if H(G) := vertical bar G vertical bar tau(G)/sigma(G) is an integer. In this paper, all finite groups for which 1 <= H(G) <= 2 have been characterized. Harmonic groups of order pq and of order pqr, where p < q < r are primes, are also classified. Moreover, it has been shown that if G is harmonic and G not congruent to C-6, then tau(G) >= 6.

引用

页码：33 / 43

页数：11

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