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A Characterization of Metacyclic p-Groups by Counting Subgroups

被引：0
|
作者：
Zhang, Qinhai [1 ]
机构：
[1] Shanxi Normal Univ, Dept Math, Linfen 041004, Shanxi, Peoples R China
来源：
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON ALGEBRA 2010: ADVANCES IN ALGEBRAIC STRUCTURES | 2012年
关键词：
Metacyclic p-groups; Counting subgroups; Regular p-groups; p(s)-abelian p-groups;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Assume G is a group of order p(n). s(k)(G) and n(k)(G) denote the number of subgroups and normal subgroups of order p(k) of G, respectively. In this paper, we obtained the following result: Let G be a metacyclic p-group of order odd prime and H a finite p-group. If s(k) (G) = s(k) (H) and n(k)(G) = n(k)(H) for arbitrary a natural number k, then G congruent to H.
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页码：713 / 720
页数：8
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