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Profinite Groups (2000)
| Citations: | 101 - 5 self |
BibTeX
@MISC{Ribes00profinitegroups,
author = {Luis Ribes and Katherine Stevenson and Pavel Zalesskii},
title = {Profinite Groups},
year = {2000}
}
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Abstract
Abstract. Recently, it has been shown by Harbater and Stevenson that a profinite group G is free profinite of infinite rank m if and only if G is projective and m-quasifree. The latter condition requires the existence of m distinct solutions to certain embedding problems for G. In this paper we provide several new non-trivial examples of m-quasifree groups, projective and non-projective. Our main result is that open subgroups of m-quasifree groups are m-quasifree. A recent characterization of free profinite groups due to Harbater and Stevenson [Theorem 2.1, HS] establishes that a profinite group G is free profinite of infinite rank m if and only if (i) G is projective, and
