A non-abelian free pro-p group is not linear over a local field

被引：9

作者：

Barnea, Y ^{[1
]}

Larsen, M

机构：

[1] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel

[2] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

来源：

JOURNAL OF ALGEBRA | 1999年 / 214卷 / 01期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1006/jabr.1998.7682

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we show that a (non-abelian) free pro-p group cannot be obtained as a closed subgroup of GL(n)(F), where F is a non-archimedean local held and n is arbitrary. Using a theorem of E. I. Zel'manov we deduce some group theoretic properties of linear pro-p groups over a local field. Our main tool is a recent theorem by Pink characterizing compact subgroups of GL(n)(F). (C) 1999 Academic Press.

引用

页码：338 / 341

页数：4

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