کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4667548 1345465 2007 56 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Primitives and central detection numbers in group cohomology
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Primitives and central detection numbers in group cohomology
چکیده انگلیسی

Fix a prime p. Given a finite group G, let H∗(G) denote its mod p cohomology. In the early 1990s, Henn, Lannes, and Schwartz introduced two invariants d0(G) and d1(G) of H∗(G) viewed as a module over the mod p Steenrod algebra. They showed that, in a precise sense, H∗(G) is respectively detected and determined by Hd(CG(V)) for d⩽d0(G) and d⩽d1(G), with V running through the elementary abelian p-subgroups of G.The main goal of this paper is to study how to calculate these invariants. We find that a critical role is played by the image of the restriction of H∗(G) to H∗(C), where C is the maximal central elementary abelian p-subgroup of G. A measure of this is the top degree e(G) of the finite dimensional Hopf algebra H∗(C)⊗H∗(G)Fp, a number that tends to be quite easy to calculate.Our results are complete when G has a p-Sylow subgroup P in which every element of order p is central. Using the Benson–Carlson duality, we show that in this case, d0(G)=d0(P)=e(P), and a similar exact formula holds for d1. As a bonus, we learn that He(G)(P) contains nontrivial essential cohomology, reproving and sharpening a theorem of Adem and Karagueuzian.In general, we are able to show that d0(G)⩽max{e(CG(V))|V

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 216, Issue 1, 1 December 2007, Pages 387-442