✦ LIBER ✦
A Non-abelian Free Pro-pGroup Is Not Linear over a Local Field
✍ Scribed by Y Barnea; M Larsen
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 51 KB
- Volume
- 214
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
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 field 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 .