Geodesic
On the differentials in the spectral sequence of a group extension
Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 49-63 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $1\to A\to G\to B\to1$ be a group extension in which $A$ is a torsion-free Abelian group. The concept of the $q$th-order characteristic class is introduced. This is an exact sequence of length 2 defined explicitly in terms of the original extension, and it coincides with the usual characteristic class when $q=0$. The main result is that the differentials $d^2_{pq}$ in the spectral sequence of the extension converging to the homology $H_*(G,Z)$ coincide with multiplication by the $q$th-order characteristic class. Analogous results can be formulated also for cohomology. Bibliography: 11 titles. 
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Yu. V. Kuz'min. On the differentials in the spectral sequence of a group extension. Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 49-63. http://geodesic.mathdoc.fr/item/SM_1988_61_1_a3/

[1] Hochschild C., Serre J. P., “Cohomology of group extensions”, Trans. Amer. Math. Soc., 74 (1953), 110–134 | DOI | MR | Zbl

[2] Maklein S., Gomologiya, Mir, M., 1966

[3] Golod E. S., “O koltse kogomologii konechnoi $p$-gruppy”, DAN SSSR, 125:4 (1959), 703–706 | MR | Zbl

[4] Venkov B. B., “Algebry kogomologii nekotorykh klassifitsiruyuschikh prostranstv”, DAN SSSR, 127 (1959), 943–944 | MR | Zbl

[5] Evens L., “The cohomology ring of a finite group”, Trans. Amer. Math. Soc., 101 (1961), 224–239 | DOI | MR | Zbl

[6] Kropholler P. H., “O finitely generated soluble groups with no large wreath product sections”, Proc. London Math. Soc., 49:3 (1984), 155–169 | DOI | MR | Zbl

[7] Kuzmin Yu. V., “Elementy poryadka 2 v svobodnoi tsentralno-razreshimoi gruppe”, Matem. zametki, 37:5 (1985), 643–652 | MR

[8] Charlap L., Vasquer A., “The cohomology of group extentions”, Trans. Amer. Math. Soc., 124 (1966), 24–40 | DOI | MR | Zbl

[9] Charlap L., Vasquer A., “Characteristic classes for modules over group”, Trans. Amer. Math. Soc., 137 (1969), 533–549 | DOI | MR | Zbl

[10] Sah Chin Han, “Cohomology of split group extensions”, J. Algebra, 29:2 (1974), 255–302 | DOI | MR | Zbl

[11] Hilton P., Stammbach U., “On the differentials in the L–H–S spectral sequence”, Bull. Amer. Math. Soc., 79:4 (1973), 796–799 | DOI | MR | Zbl