A Non-abelian Free Pro-p Group Is Not Linear Over a Local Field
نویسندگان
چکیده
In this paper we show that a (non-abelian) free pro-p group cannot be obtained as a closed subgroup of GLn(F ), where F is a nonarchimedean 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 GLn(F ). ∗Partially supported by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany). †Partially supported by NSF grant DMS-9400833 and a grant from the Sloan Foundation.
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