New characterizations of σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-nilpotent finite groups

被引：0
作者：
Viachaslau I. Murashka
Alexander F. Vasil’ev
机构：
[1] Francisk Skorina Gomel State University,Faculty of Mathematics and Technologies of Programming
来源：
Ricerche di Matematica | 2024年 / 73卷 / 1期
关键词：
Finite group; Generalized Fitting subgroup; Hereditary formation; -; -subnormal subgroup; -nilpotent group; Primary 20D25; Secondary 20F17; 20F19;
D O I：
10.1007/s11587-021-00627-8
中图分类号：
学科分类号：
摘要：
Let σ={πi∣i∈I}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sigma =\{\pi _i\mid i\in I\}$$\end{document} be a partition of the set of all primes. We characterize the class of all σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-nilpotent groups as a hereditary formation F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {F}}$$\end{document} that contains every group G all whose Sylow subgroups are K-F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {F}}$$\end{document}-subnormal in their product with the generalized Fitting subgroup F∗(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {F}^*(G)$$\end{document}.
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页码：611 / 618
页数：7
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