On the Structure of Groups Whose Non-normal Subgroups Are Core-Free

被引：0
作者：
L. A. Kurdachenko
A. A. Pypka
I. Ya. Subbotin
机构：
[1] Oles Honchar Dnipro National University,Department of Geometry and Algebra
[2] National University,Department of Mathematics and Natural Sciences
来源：
Mediterranean Journal of Mathematics | 2019年 / 16卷
关键词：
Normal subgroup; core-free subgroup; Dedekind group; monolithic group; Primary 20E34; Secondary 20D15; 20D25; 20E07; 20F19; 20F50;
D O I：
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摘要：
A subgroup H of a group G is called core-free if CoreG(H)=⋂x∈GHx=⟨1⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{Core}}_{G}(H)=\bigcap \nolimits _{x\in G}H^{x}=\langle 1\rangle $$\end{document}. In the current article, we study the groups in which every subgroup is either normal or core-free.
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