Profinite groups with restricted centralizers of π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}-elements

被引：0
作者：
Cristina Acciarri
Pavel Shumyatsky
机构：
[1] Università degli Studi di Modena e Reggio Emilia,Dipartimento di Scienze Fisiche, Informatiche e Matematiche
[2] University of Brasilia,Department of Mathematics
来源：
Mathematische Zeitschrift | 2022年 / 301卷 / 1期
关键词：
Profinite groups; Centralizers; -elements; FC-groups; 20E18; 20F24;
D O I：
10.1007/s00209-021-02955-9
中图分类号：
学科分类号：
摘要：
A group G is said to have restricted centralizers if for each g in G the centralizer CG(g)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_G(g)$$\end{document} either is finite or has finite index in G. Shalev showed that a profinite group with restricted centralizers is virtually abelian. Given a set of primes π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}, we take interest in profinite groups with restricted centralizers of π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}-elements. It is shown that such a profinite group has an open subgroup of the form P×Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P\times Q$$\end{document}, where P is an abelian pro-π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} subgroup and Q is a pro-π′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi '$$\end{document} subgroup. This significantly strengthens a result from our earlier paper.
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页码：1039 / 1045
页数：6
相关论文
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