×

Topological methods in abstract algebra. Cohomology theory of groups. (English) Zbl 0031.34202


PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Emil Artin, Cecil J. Nesbitt, and Robert M. Thrall, Rings with Minimum Condition, University of Michigan Publications in Mathematics, no. 1, University of Michigan Press, Ann Arbor, Mich., 1944. · Zbl 0060.07701
[2] R. Baer, Automorphismen von Erweiterungsgruppen, Actualités scientifiques et Industrielles, No. 205, Paris, 1935. · JFM 61.1020.02
[3] A. L. Blakers, Some relations between homology and homotopy groups, Ann. of Math. (2) 49 (1948), 428 – 461. · Zbl 0040.25701
[4] H. Cartan and S. Eilenberg, Products of groups and complexes (in preparation).
[5] Claude Chevalley and Samuel Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85 – 124. · Zbl 0031.24803
[6] Beno Eckmann, Der Cohomologie-Ring einer beliebigen Gruppe, Comment. Math. Helv. 18 (1946), 232 – 282 (German). · Zbl 0061.40705
[7] Beno Eckmann, On complexes over a ring and restricted cohomology groups, Proc. Nat. Acad. Sci. U. S. A. 33 (1947), 275 – 281. · Zbl 0045.44102
[8] Beno Eckmann, On infinite complexes with automorphisms, Proc. Nat. Acad. Sci. U. S. A. 33 (1947), 372 – 376. · Zbl 0030.37501
[9] Samuel Eilenberg, Homology of spaces with operators. I, Trans. Amer. Math. Soc. 61 (1947), 378 – 417; errata, 62, 548 (1947). · Zbl 0034.11001
[10] Samuel Eilenberg, Relations between cohomology groups in a complex, Comment. Math. Helv. 21 (1948), 302 – 320. · Zbl 0031.18103
[11] Samuel Eilenberg and Saunders MacLane, Group extensions and homology, Ann. of Math. (2) 43 (1942), 757 – 831. · Zbl 0061.40602
[12] Samuel Eilenberg and Saunders MacLane, Relations between homology and homotopy groups, Proc. Nat. Acad. Sci. U. S. A. 29 (1943), 155 – 158. · Zbl 0061.40701
[13] Samuel Eilenberg and Saunders MacLane, Relations between homology and homotopy groups of spaces, Ann. of Math. (2) 46 (1945), 480 – 509. · Zbl 0061.40702
[14] Samuel Eilenberg and Saunders MacLane, Determination of the second homology and cohomology groups of a space by means of homotopy invariants, Proc. Nat. Acad. Sci. U. S. A. 32 (1946), 277 – 280. · Zbl 0061.40707
[15] Samuel Eilenberg and Saunders MacLane, Cohomology theory in abstract groups. I, Ann. of Math. (2) 48 (1947), 51 – 78. · Zbl 0029.34001
[16] Samuel Eilenberg and Saunders MacLane, Cohomology theory in abstract groups. II. Group extensions with a non-Abelian kernel, Ann. of Math. (2) 48 (1947), 326 – 341. · Zbl 0029.34101
[17] Samuel Eilenberg and Saunders MacLane, Algebraic cohomology groups and loops, Duke Math. J. 14 (1947), 435 – 463. · Zbl 0029.34102
[18] Samuel Eilenberg and Saunders MacLane, Cohomology and Galois theory. I. Normality of algebras and Teichmüller’s cocycle, Trans. Amer. Math. Soc. 64 (1948), 1 – 20. · Zbl 0031.34301
[19] Samuel Eilenberg and Saunders MacLane, Homology of spaces with operators. II, Trans. Amer. Math. Soc. 65 (1949), 49 – 99. · Zbl 0034.11101
[20] S. Eilenberg and S. MacLane, Relations between homology and homotopy groups of spaces. II, Ann. of Math. (in print). · Zbl 0036.12602
[21] Hans Freudenthal, Der Einfluss der Fundamentalgruppe auf die Bettischen Gruppen, Ann. of Math. (2) 47 (1946), 274 – 316 (German). · Zbl 0061.40706
[22] G. Hochschild, On the cohomology groups of an associative algebra, Ann. of Math. (2) 46 (1945), 58 – 67. · Zbl 0063.02029
[23] G. Hochschild, On the cohomology theory for associative algebras, Ann. of Math. (2) 47 (1946), 568 – 579. · Zbl 0063.02030
[24] G. Hochschild, Cohomology and representations of associative algebras, Duke Math. J. 14 (1947), 921 – 948. · Zbl 0029.34201
[25] Heinz Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv. 14 (1942), 257 – 309 (German). · Zbl 0027.09503
[26] Heinz Hopf, Über die Bettischen Gruppen, die zu einer beliebigen Gruppe gehören, Comment. Math. Helv. 17 (1945), 39 – 79 (German). · Zbl 0061.40703
[27] Heinz Hopf, Beiträge zur Homotopietheorie, Comment. Math. Helv. 17 (1945), 307 – 326 (German). · Zbl 0061.40704
[28] Roger C. Lyndon, The cohomology theory of group extensions, Duke Math. J. 15 (1948), 271 – 292. · Zbl 0031.19802
[29] R. G. Lyndon, New proof for a theorem of Eilenberg and MacLane, Ann. of Math. (in print). · Zbl 0040.25602
[30] Saunders MacLane, Symmetry of algebras over a number field, Bull. Amer. Math. Soc. 54 (1948), 328 – 333. , https://doi.org/10.1090/S0002-9904-1948-08996-0 Saunders MacLane, A nonassociative method for associative algebras, Bull. Amer. Math. Soc. 54 (1948), 897 – 902. · Zbl 0032.10801
[31] S. MacLane, Cohomology theory in abstract groups. III, Operator homomorphisms of kernels, Ann. of Math. (in print). · Zbl 0039.25703
[32] O. Teichmüller, Ueber die sogenannte nichtkommutative Galoissche Theorie und die Relation \xi \lambda ,\mu ,\nu \xi \lambda ,\mu \nu ,\pi \xi \lambda ,\nu ,\pi =\xi \lambda ,\mu ,\nu \pi \xi \lambda \mu ,\nu ,\pi , Deutsche Mathematik vol. 5 (1940) pp. 138-149. · Zbl 0023.19805
[33] Hsien-Chung Wang, Some examples concerning the relations between homology and homotopy groups, Nederl. Akad. Wetensch., Proc. 50 (1947), 873 – 875 = Indagationes Math. 9, 384 – 386 (1947). · Zbl 0030.27203
[34] George W. Whitehead, On spaces with vanishing low-dimensional homotopy groups, Proc. Nat. Acad. Sci. U. S. A. 34 (1948), 207 – 211. · Zbl 0031.28601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.