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Maximal subgroups and strong completeness of profinite groups

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Abstract

It is proved that all subgroups of finite index in a profinite group G are open if and only if G has only countably many abstract maximal subgroups of finite index.

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References

  1. Smith M.G., Wilson J.S.: On subgroups of finite index in compact Hausdorff groups. Arch. Math. (Basel) 80, 123–129 (2003)

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  3. N. Nikolov, D. Segal, On finitely generated profinite groups. I. Strong completeness and uniform bounds; II. Products in quasisimple groups. Ann. of Math. 165 (2007) 171–238; 239–273

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  1. Oxford, United Kingdom

    John S. Wilson

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  1. John S. Wilson
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Correspondence to John S. Wilson.

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Wilson, J.S. Maximal subgroups and strong completeness of profinite groups. Arch. Math. 105, 401–404 (2015). https://doi.org/10.1007/s00013-015-0830-x

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  • DOI: https://doi.org/10.1007/s00013-015-0830-x

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