# Name of the Marshall Hall paper in which he proved that the intersection of all subgroups of a fixed finite index is again finite index?

can someone please tell me? I couldn't find a reference in the paper I was reading.

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Note that this fact is only true in finitely generated groups. –  HJRW Feb 16 '10 at 5:21

Subgroups of finite index in free groups. Canadian J.Math., 1:187–190, 1949.

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This is not a result of Hall; Hall counted precisely the number of such subgroups. Here are links to the paper: cms.math.ca/cjm/v1/p187 ams.org/mathscinet-getitem?mr=28836 –  Jack Schmidt Feb 16 '10 at 5:00
Thanks for the help. –  david mccune Feb 16 '10 at 6:12