中北大学学报（自然科学版）2017，Vol.38Issue(2)：99-102,4.DOI:10.3969/j.issn.1673-3193.2017.02.001
关于内幂零群结构定理的一个注记
A Note on the Structural Theorem of Minimal Nonnilpotent Groups
摘要
Abstract
Minimal nontrivial actions were studied.The equivalent conditions of irreducibility of linear transformations of finite dimensional vector spaces over a field F were generalized to the elementary abelian p-groups.Combining with the concept of minimal nontrivial actions,a necessary and sufficient condition of Hall-Higman's theorem was obtained.As a corollary,a new characterization of the minimal nontrivial actions was given.This new characterization was applied to study when the induced action of a p'-automorphism of a p-group on the Frattini quotient is irreducible.Furthermore,a new proof of Schmidt's theorem is obtained.As a consequence,a new criterion (with a simplified proof) of minimal nonnilpotent groups is developed.关键词
内幂零群/极小非平凡作用/不可约/自同构Key words
minimal nonnilpotent group/minimal nontrivial action/irreducible/automorphism分类
数理科学引用本文复制引用
王玉婷,郝成功..关于内幂零群结构定理的一个注记[J].中北大学学报（自然科学版）,2017,38(2):99-102,4.基金项目
山西省自然科学基金资助项目(201601D011006) （201601D011006）
