Homology in Group Theory

Homology in Group Theory

Urs Stammbach, "Homology in Group Theory"
1973 | pages: 186 | ISBN: 3540065695, 0387065695 | PDF | 3,6 mb

The purpose of these Notes is twofold. First, the homological algebraist may learn something about applications of homology theory to group theory, second, the group theorist may see what homological methods are able to achieve in his own field.
Chapter I introduces the reader to some basic notions in group theory. In Chapter II we have assembled the basic facts about the (co)homology of groups. Together with Chapter VI of Hilton-Stammbach [43] this will serve as a reasonable complete introduction to the (co)homology theory of groups as far as it is needed for these Notes.
Chapters III, IV, V, VI form the core of this volume. We present applications in four different but not entirely disjoint areas: extensions with abelian kernel in a variety, theorems on the lower central series, theorems on central extensions, localization of nilpotent groups.




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