Dissertation/Thesis Abstract

Cohomology of Z-free resolutions of p-groups
by Hoang, Quang M., Ph.D., Princeton University, 2009, 67; 3374783
Abstract (Summary)

Let p be an odd prime. This dissertation uses the p-exponent lower central series to define the concept of [special characters omitted]-free resolutions of p-groups. A [special characters omitted]-free resolution of a p-group G is a torsion free nilpotent group together with a epimorphism f : G satisfying certain conditions. Then BG¯ is a manifold, therefore the structure of cohomology of is simpler than that of G. We will show that any p-group has a [special characters omitted]-free resolution. In the case of the unipotent group U( n; [special characters omitted]), an example of [special characters omitted]-free resolution is U(n; [special characters omitted]). Although a [special characters omitted]-free resolution of a p-group G is not unique, we show that when G has p-nilpotency degree 2, H*(; [special characters omitted]) is independent of choices of . Finally, we calculated cohomology of a family of [special characters omitted]-free resolutions n for some p-groups Vn and show that the cohomology map H*(Vn; [special characters omitted]) → H*(n; [special characters omitted]) is onto.

Indexing (document details)
Advisor: Browder, William
School: Princeton University
School Location: United States -- New Jersey
Source: DAI-B 70/09, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Cohomology, Z-free resolutions, p-groups
Publication Number: 3374783
ISBN: 978-1-109-36395-1
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