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In mathematics, the Hilbert–Smith conjecture is concerned with the transformation groups of manifolds; and in particular with the limitations on topological groups ''G'' that can act effectively (faithfully) on a (topological) manifold ''M''. Restricting to ''G'' which are locally compact and have a continuous, faithful group action on ''M'', it states that ''G'' must be a Lie group. Because of known structural results on ''G'', it is enough to deal with the case where ''G'' is the additive group ''Zp'' of p-adic integers, for some prime number ''p''. An equivalent form of the conjecture is that ''Zp'' has no faithful group action on a topological manifold. The naming of the conjecture is for David Hilbert, and the American topologist Paul A. Smith. It is considered by some to be a better formulation of Hilbert's fifth problem, than the characterisation in the category of topological groups of the Lie groups often cited as a solution. In 2013, John Pardon proved the three-dimensional case of the Hilbert–Smith conjecture. ==References== * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hilbert–Smith conjecture」の詳細全文を読む スポンサード リンク
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