The Subgroups of Finite Metacyclic Groups  

作　　者：Xu YANG 

机构地区：[1]School of Mathematical Sciences,Fudan University,Shanghai 200433,China

出　　处：《Chinese Annals of Mathematics,Series B》2020年第2期241-266,共26页数学年刊（B辑英文版）

基　　金：the National Natural Science Foundation of China(No.11331006)。

摘　　要：In this paper, the author characterizes the subgroups of a finite metacyclic group K by building a one to one correspondence between certain 3-tuples(k, l, β) ∈ N3 and all the subgroups of K. The results are applied to compute some subgroups of K as well as to study the structure and the number of p-subgroups of K, where p is a fixed prime number. In addition, the author gets a factorization of K, and then studies the metacyclic p-groups, gives a different classification, and describes the characteristic subgroups of a given metacyclic p-group when p ≥ 3. A "reciprocity" relation on enumeration of subgroups of a metacyclic group is also given.

关 键 词：Metacyclic GROUPS SUBGROUPS Metacyclic P-GROUPS CHARACTERISTIC SUBGROUPS 

分 类 号：O152.1[理学—数学]