Published: 1955 Received: June 08, 1955Available on J-STAGE: August 29, 2006Accepted: -
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Date of correction: August 29, 2006Reason for correction: -Correction: CITATIONDetails: Right : 1) G. Hochschild and J. -P. Serre, Cohomology of group extensions, Trans. Amer. Math. Soc. 74 (1953), pp. 110-134. 2) See, S. Eilenberg and S. MacLane, Cohomology theory in abstract groups. I, Ann. of Math. 48, (1947), pp. 51-78, and G. Hochschild and J. -P. Serre, loc. cit. in 1). 3) See Appendix. 4) G. Hochschild and J. -P. Serre, loc. cit., Chap. III, §4, Theorem 2. 5) G. Hochschild and J. -P. Serre, loc. cit., Chap. III, 6, Theorem 3. 7) Chap. II, §3. 8) The homology and the cohomology theory can be built up based on a few fundamental properties of tensor product and the group of homomorphisms, as is shown e. g. in S. Eilenberg and N. Steenrod, Foundations of algebraic topology. Princeton University Press, 1952. Homg (B⊗η A, C)≅Homη (A, Homg (B, C)) is one of them, where A is an η-module, C a g-module and B a (g, η)-double module. 9) Z(g) is considered as a right g-module by the right multiplication. 10) Cf. S. Eilenberg and S. MacLane, On the groups H (II, n), I. Ann. of Math. 58 (1953), pp. 55-106, where the case of abelian groups is treated.
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