Bulletin of the American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

Topological methods in abstract algebra. cohomology theory of groups

Author(s): Samuel Eilenberg
Journal: Bull. Amer. Math. Soc. 55 (1949), Part 1:3-37.
MathSciNet review: 0030523
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References | Additional information

References:

1.: E. Artin, C. J. Nesbitt and R. M. Thrall, Rings with minimum conditions, University of Michigan Press, Ann Arbor, 1944. MR 10543
2.: R. Baer, Automorphismen von Erweiterungsgruppen, Actualités scientifiques et Industrielles, No. 205, Paris, 1935.
3.: A. L. Blakers, Some relations between homology and homotopy groups, Ann. of Math. vol. 49 (1948) pp. 428-461. MR 24132
4.: H. Cartan and S. Eilenberg, Products of groups and complexes (in preparation).
5.: C. Chevalley and S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. vol. 63 (1948) pp. 85-124. MR 24908
6.: B. Eckmann, Der Cohomologie-Ring einer beliebigen Gruppe, Comment. Math. Helv. vol. 18 (1945-1946) pp. 232-282. MR 17536
7.: B. Eckmann, On complexes over a ring and restricted cohomology groups, Proc. Nat. Acad. Sci. U.S.A. vol. 33 (1947) pp. 275-281. MR 22668
8.: B. Eckmann, On infinite complexes with automorphisms, Proc. Nat. Acad. Sci. U.S.A. vol. 33 (1947) pp. 372-376. MR 23057
9.: S. Eilenberg, Homology of spaces with operators. I, Trans. Amer. Math. Soc. vol. 61 (1947) pp. 378-417; Errata vol. 62 (1947) p. 548. MR 21313
10.: S. Eilenberg, Relations between cohomology groups in a complex, Comment. Math. Helv. vol. 21 (1948) pp. 302-320. MR 26798
11.: S. Eilenberg and S. MacLane, Group extensions and homology, Ann. of Math. vol. 43 (1942) pp. 757-831. MR 7108
12.: S. Eilenberg and S. MacLane, Relations between homology and homotopy groups, Proc. Nat. Acad. Sci. U.S.A. vol. 29 (1943) pp. 155-158. MR 7982
13.: S. Eilenberg and S. MacLane, Relations between homology and homotopy groups of spaces, Ann. of Math. vol. 46 (1945) pp. 480-509. MR 13312
14.: S. Eilenberg and S. MacLane, Determination of the second homology and cohomology groups of a space by means of homotopy invariants, Proc. Nat. Acad. Sci. U.S.A. vol. 32 (1946) pp. 277-280. MR 19307
15.: S. Eilenberg and S. MacLane, Cohomology theory in abstract groups. I, Ann. of Math. vol. 48 (1947) pp. 51-78. MR 19092
16.: S. Eilenberg and S. MacLane, Cohomology theory in abstract groups. II, Group extensions with a non-Abelian kernel, Ann. of Math. vol. 48 (1947) pp. 326-341. MR 20996
17.: S. Eilenberg and S. MacLane, Algebraic cohomology groups and loops, Duke Math. J. vol. 14 (1947) pp. 435-463. MR 21939
18.: S. Eilenberg and S. MacLane, Cohomology and Galois Theory. I. Normality of algebras and Teichmüller's cocycle, Trans. Amer. Math. Soc. vol. 64 (1948) pp. 1-20. MR 25443
19.: S. Eilenberg and S. MacLane, Homology of spaces with operators. II, Trans. Amer. Math. Soc. vol. 65 (1949). MR 33001
20.: S. Eilenberg and S. MacLane, Relations between homology and homotopy groups of spaces. II, Ann. of Math. (in print).
21.: H. Freudenthal, Der Einfluss der Fundamentalgruppe auf die Bettische Gruppen, Ann. of Math. vol. 47 (1946) pp. 274-316. MR 17535
22.: G. Hochschild, On the cohomology groups of an associative algebra, Ann. of Math. vol. 46 (1945) pp. 58-67. MR 11076
23.: G. Hochschild, On the cohomology theory for associative algebras, Ann. of Math. vol. 47 (1946) pp. 568-579. MR 16762
24.: G. Hochschild, Cohomology and representations of associative algebras, Duke Math. J. vol. 14 (1947) pp. 921-948. MR 22842
25.: H. Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv. vol. 14 (1942) pp. 257-309; Nachtrag zu... vol. 15 (1943) pp. 27-32.[Note] MR 6510
26.: H. Hopf, Ueber die Bettische Gruppen die zu einer beliebigen Gruppe gehören, Comment. Math. Helv. vol. 17 (1945) pp. 39-79. MR 12229
27.: H. Hopf, Beiträge zur Homotopietheorie, Comment. Math. Helv. vol. 17 (1945) pp. 307-333. MR 12544
28.: R. G. Lyndon, The cohomology theory of group extensions, Duke Math. J. vol. 15 (1948) pp. 271-292. MR 25468
29.: R. G. Lyndon, New proof for a theorem of Eilenberg and MacLane, Ann. of Math. (in print).
30.: S. MacLane, Symmetry of algebras over a number field, Bull. Amer. Math. Soc. vol. 54 (1948) pp. 328-333. MR 25442; 31 S. MacLane, A non-associative method for associative algebras, Bull. Amer. Math. Soc. vol. 54 (1948) pp. 897-902. MR 26993
32.: S. MacLane, Cohomology theory in abstract groups. III, Operator homomorphisms of kernels, Ann. of Math. (in print).
33.: O. Teichmüller, Ueber die sogenannte nichtkommutative Galoissche Theorie und die Relation ξλ,μ,νξλ,μν,πξ^λ,ν,π=ξλ,μ,νπξλμ,ν,π, Deutsche Mathematik vol. 5 (1940) pp. 138-149.
34.: H. S. Wang, Some examples concerning the relations between homology and homotopy groups, K. Nederlandsche Akademie van Wetenschappen, Proceedings vol. 50 (1947) pp. 873-875 = Indagationes Mathematical vol. 9 (1947) pp. 384-386. MR 22349
35.: G. W. Whitehead, On spaces with vanishing low-dimensional homotopy groups, Proc. Nat. Acad. Sci. U. S. A. vol. 34 (1948) pp. 207-211. MR 28027

Additional Information:

DOI: 10.1090/S0002-9904-1949-09161-9
PII: S 0002-9904(1949)09161-9

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