Le cinquième problème de Hilbert. État de la question en 1951
Serre, Jean-Pierre
Bulletin de la Société Mathématique de France, Tome 80 (1952), p. 1-10 / Harvested from Numdam
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@article{BSMF_1952__80__1_0,
     author = {Serre, Jean-Pierre},
     title = {Le cinqui\`eme probl\`eme de Hilbert. \'Etat de la question en 1951},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     volume = {80},
     year = {1952},
     pages = {1-10},
     doi = {10.24033/bsmf.1422},
     mrnumber = {14,136a},
     zbl = {0046.25302},
     mrnumber = {49205},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/BSMF_1952__80__1_0}
}

Serre, Jean-Pierre. Le cinquième problème de Hilbert. État de la question en 1951. Bulletin de la Société Mathématique de France, Tome 80 (1952) pp. 1-10. doi : 10.24033/bsmf.1422. http://gdmltest.u-ga.fr/item/BSMF_1952__80__1_0/

[1] L. E. J. Brouwer, Die Theorie der endlichen kontinuerlichen Gruppen, unabhangig von den Axiomen von Lie (Math. Ann., t. 67, 1909, p. 246-267). | JFM 40.0194.01

[2] L. E. J. Brouwer, Ibid., t. 69, 1910, p. 181-203. | JFM 41.0181.03

[3] C. Chevalley, Two theorems on solvable topological groups (Lectures in Topology, Michigan, 1941). | MR 3,135a | Zbl 0063.00839

[4] C. Chevalley, Theory of Lie groups, Princeton, 1946. | Zbl 0063.00842

[5] A. M. Gleason, Square roots in locally euclidean groups (Bull. Amer. Math. Soc., t. 55, 1949, p. 446-449). | MR 10,507c | Zbl 0041.16002

[6] A. M. Gleason, Spaces with a compact Lie group of transformations (Proc. Amer. Math. Soc., t. 1, 1950, p. 35-43). | MR 11,497e | Zbl 0041.36207

[7] A. M. Gleason, The structure of locally compact groups (Duke Math. Journ., t. 18, 1951, p. 85-110). | MR 12,589a | Zbl 0044.01901

[8] A. M. Gleason, Arcs in locally compact groups (Proc. Nat. Acad. Sc. U.S.A., t. 36, 1950, p. 663-667). | MR 12,391b | Zbl 0040.15301

[9] D. Hilbert, Mathematische Probleme (Gott. Nachr., 1900, p. 253-297). | JFM 31.0068.03

[10] W. Hurewicz and H. Wallman, Dimension Theory, Princeton, 1941. | JFM 67.1092.03 | MR 3,312b | Zbl 0060.39808

[11] K. Iwasawa, On some types of topological groups (Ann. Math., t. 50, 1949, p. 507-558). | MR 10,679a | Zbl 0034.01803

[12] Von Kerekjarto, Geometrische Theorie der Zweigliedrigen kontinuerlichen Gruppen Hamb. Abh., t. 8, 1931, p. 107-114). | JFM 56.1026.03

[13] M. Kuranishi, On euclidean local groups satisfying certain conditions (Proc. Amer. Math. Soc., t. 1, 1950, p. 372-380). | MR 12,77f | Zbl 0038.01701

[14] M. Kuranishi, On conditions of differentiability of locally compact groups (Nagoya Math. Journ., t. 1, 1950, p. 71-81). | MR 12,391a | Zbl 0037.30502

[15] D. Montgomery, A theorem on locally euclidean groups (Ann. Math., 48, 1947, p. 650-659). | MR 9,174e | Zbl 0030.10802

[16] D. Montgomery, Connected one dimensional groups (Ann. Math., t. 49, 1948, p. 110-117). | MR 9,496b | Zbl 0030.01001

[17] D. Montgomery, Analytic parameters in three dimensional groups (Ann. Math., t. 49, 1948, p. 118-131). | MR 9,496c | Zbl 0030.01002

[18] D. Montgomery, Dimension of factor spaces (Ann. Math., t. 49, 1948, p. 373-378). | MR 9,566c | Zbl 0031.24802

[19] D. Montgomery, Connected two dimensional groups (Ann. Math., t. 51, 1950, p. 262-277). | MR 11,497c | Zbl 0037.15601

[20] D. Montgomery, Locally homogeneous spaces (Ann. Math., t. 52, 1950, p. 261-271). | MR 13,319e | Zbl 0038.36201

[21] D. Montgomery, Finite dimensional groups (Ann. Math., t. 52, 1950, p. 591-605). | MR 12,673e | Zbl 0041.36310

[22] D. Montgomery, and L. Zippin, Existence of subgroups isomorphic to the real numbers (Ann. Math., t. 53, 1951, p. 298-326). | MR 13,911f | Zbl 0045.31202

[23] D. Montgomery, and L. Zippin, Bull. Amer. Math. Soc., t. 57, p. 75, Abstract 53 t.

[24] D. Montgomery, and L. Zippin, Ibid., p. 145, Abstract 176 t.

[25] J. Von Neumann, Die Einführung analytischer Parameter in topologische Gruppen (Ann. Math., t. 34, 1933, p. 170-190). | JFM 59.0433.01 | Zbl 0006.30003

[26] L. Pontrjagin, The theory of topological commutative groups (Ann. Math., t. 35, 1934, p. 361-388). | JFM 60.0362.02 | Zbl 0009.15601

[27] L. Pontrjagin, Topological groups, Princeton, 1939. | JFM 65.0872.02

[28] O. Schreier, Abstrakte kontinuerliche Gruppen (Hamb. Abh., t. 4, 1926, p. 15-32). | JFM 51.0112.04

[29] P. A. Smith, Transformations of finite period. III. Newman's theorem (Ann. Math., t. 42, 1941, p. 446-458). | JFM 67.0743.01 | MR 2,324c | Zbl 0027.26602

[30] P. A. Smith, Periodic and nearly periodic transformations (Lectures in Topolody, Michigan, 1941). | MR 3,133c | Zbl 0063.07091

[31] A. Weil, L'intégration dans les groupes topologiques et ses applications, Paris, 1940. | JFM 66.1205.02 | MR 3,198b | Zbl 0063.08195

[32] R. L. Wilder, Topology of Manifolds, Colloquium, 1949. | MR 10,614c | Zbl 0039.39602

[33] H. Yamabe, Note on locally compact groups (Osaka Math. Journ., t. 3, 1951, p. 77-82). | MR 13,13a | Zbl 0043.03202