Citation
Y. Barnea et M. Larsen, A non-abelian free pro-p group is not linear over a local field, J ALGEBRA, 214(1), 1999, pp. 338-341
Citations number
10
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF ALGEBRA
ISSN journal
00218693
→ ACNP
Volume
214
Issue
1
Year of publication
1999
Pages
338 - 341
Database
ISI
SICI code
0021-8693(19990401)214:1<338:ANFPGI>2.0.ZU;2-R
Abstract
In this paper we show that a (non-abelian) free pro-p group cannot be obtai
ned as a closed subgroup of GL(n)(F), where F is a non-archimedean local he
ld and n is arbitrary. Using a theorem of E. I. Zel'manov we deduce some gr
oup theoretic properties of linear pro-p groups over a local field. Our mai
n tool is a recent theorem by Pink characterizing compact subgroups of GL(n
)(F). (C) 1999 Academic Press.