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Fundamental Exact Sequences in (co)-Homology for Non-Normal Subgroups

Published online by Cambridge University Press:  22 January 2016

Tadasi Nakayama
Tadasi Nakayama*
Affiliation:
Nagoya University
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In this paper we prove the fundamental exact sequence in (co)homology for non-normal subgroups announced in our previous note [8]: Let H be a subgroup of a group G. If M is a G-module and if, for a natural number n, Hm(U, M) = 0 for m = 1, …, n - 1 and for every subgroup U of H which is an intersection of conjugates of H in G, then we have an exact sequence

the significance of the maps and the group Hn(H, M, M)1 will be explained below. (We have a dual result for cohomology groups).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 18 , April 1961 , pp. 63 - 92
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1961

References

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