Geodesic
Cohomology Theory for Non-Normal Subgroups and Non-Normal Fields*
Glasgow mathematical journal, Tome 2 (1954) no. 2, pp. 66-76

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a finite group, H an arbitrary subgroup (i.e., not necessarily normal); we decompose G as a union of left cosets modulo H:choosing fixed coset representatives v. In this paper we construct a “coset space complex” and assign cohomology groups; Hr([G: H], A), to it for all coefficient modules A and all dimensions, -∞<r<∞. We show that ifis an exact sequence of coefficient modules such that H1U, A')= 0 for all subgroups U of H, then a cohomology group sequencemay be defined and is exact for -∞<r<∞. We also provide a link between the cohomology groups Hr([G: H], A) and the cohomology groups of G and H; namely, we prove that if Hv(U, A)= 0 for all subgroups U of H and for v = 1, 2, ..., n–1, then the sequenceis exact, where the homomorphisms of the sequence are those induced by injection, inflation and restriction respectively. 
Cohomology Theory for Non-Normal Subgroups and Non-Normal Fields*. Glasgow mathematical journal, Tome 2 (1954) no. 2, pp. 66-76. doi: 10.1017/S2040618500033050
@misc{10_1017_S2040618500033050,
     title = {Cohomology {Theory} for {Non-Normal} {Subgroups} and {Non-Normal} {Fields*}},
     journal = {Glasgow mathematical journal},
     pages = {66--76},
     year = {1954},
     volume = {2},
     number = {2},
     doi = {10.1017/S2040618500033050},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033050/}
}
TY  - JOUR
TI  - Cohomology Theory for Non-Normal Subgroups and Non-Normal Fields*
JO  - Glasgow mathematical journal
PY  - 1954
SP  - 66
EP  - 76
VL  - 2
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033050/
DO  - 10.1017/S2040618500033050
ID  - 10_1017_S2040618500033050
ER  - 
%0 Journal Article
%T Cohomology Theory for Non-Normal Subgroups and Non-Normal Fields*
%J Glasgow mathematical journal
%D 1954
%P 66-76
%V 2
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033050/
%R 10.1017/S2040618500033050
%F 10_1017_S2040618500033050

[(1)] (1)Artin, E., Algebraic Numbers and Algebraic Functions (New York, 1951). Google Scholar

[(2)] (2)Artin, E. and Tate, J. T., Class Field Theory, Princeton seminar notes, 1951–1952, (to appear). Google Scholar

[(3)] (3)Brauer, R., “On Splitting Fields of Simple Algebras”, Annals of Math., vol. 48 (1947), pp. 79–90. Google Scholar | DOI

[(4)] (4)Eilenberg, S., “Homology of Spaces with Operators, I”, Trans. Amer. Math. Soc., vol. 61 (1947), pp. 378–417. Google Scholar | DOI

[(5)] (5)Hochschild, G. and Nakayama, T., “Cohomology in Class Field Theory”, Annals of Math., vol. 55 (1952), pp. 348–66. Google Scholar | DOI

[(6)] (6)Tate, J. T., “The Higher Dimension Cohomology Groups of Class Field Theory”, Annals of Math., vol. 56 (1952), pp. 294–7. Google Scholar | DOI

Cité par Sources :