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Deane Montgomery: Frases en inglés

“A group which has a simple structure may offer difficult questions when operating as a transformation group. For example, the ways in which a cyclic group of order 2 can operate on a manifold, even on E 3, are far from completely known.”

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Deane Montgomery

[Properties of finite-dimensional groups, Proceedings of the International Mathematical Congress held in Cambridge, Mass. in 1950, 442–446, University of Toronto Press, 1952, http://www.mathunion.org/ICM/ICM1950.2/Main/icm1950.2.0442.0446.ocr.pdf] (quote from p. 442)

“THEOREM: if G is a locally euclidean, connected, simply connected topological group of dimension n greater than one, then G contains a closed proper subgroup of positive dimension.”

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Deane Montgomery

[A theorem on locally euclidean groups, Annals of Mathematics, 1947, 650–658, 10.2307/1969132]