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From Scott's book Group Theory

$1.7.10.$ (Poincaré) The intersection of a finite number of subgroups of finite index is of finite index.

My question is: Did Poincaré prove the Theorem as stated above or something like that? I mean, was he interested in Group Theory or he proved something which resembles the theorem stated above

I would appreciate any suggestion.

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    This question is part of [this question](http://math.stackexchange.com/q/351983/49437) (with no answer). I suppose we don't need two versions of the same question open, but the system insists.2013-04-29

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