Stable splittings of classifying spaces of metacyclic p-groups, p odd
نویسندگان
چکیده
منابع مشابه
TORAL GROUPS AND CLASSIFYING SPACES OF p–COMPACT GROUPS by
It is knwon [23] that if p is odd, NpT is isomorphic to the semidirect product T oWp, and the fibration (BT )p (BNpT )p BWp has a section. The classifying spaces of NpT and other p–toral subgroups of K have been extensively used for the study of BK at the prime p, [13] etc. We note, however, that for the normalizer NT the loop space of (BNT )p need not be a p–compact toral group. In fact, if p ...
متن کاملON THE HOMOTOPY GROUPS OF p-COMPLETED CLASSIFYING SPACES
Among the generalizations of Serre’s theorem on the homotopy groups of a finite complex we isolate the one proposed by Dwyer and Wilkerson. Even though the spaces they consider must be 2-connected, we show that it can be used to both recover known results and obtain new theorems about p-completed classifying spaces.
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Remark. If G is a compact Lie group with maximal torus TG and Weyl Group WG, the finitely generated free Z-module LG = π1TG has a natural action of WG and is called the dual weight lattice of G. The group G is simple in the usual sense if and only if the center of G is trivial and the action of WG on Q ⊗ LG gives an irreducible representation of WG over Q. From this point of view 1.3 is a direc...
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A p-compact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined p-local analog of a compact Lie group. It has long been the hope, and later the conjecture, that these objects should have a classification similar to the classification of compact Lie groups. In this paper we finish the proof of this conjecture, for p an odd prime, proving that there is a one-to-one corresp...
متن کاملAutomorphisms of Metacyclic p-Groups With Cyclic Maximal Subgroups
This paper deals with the determination of the automorphism group of the metacyclic p-groups, P (p,m), given by the presentation P (p,m) = 〈x, y|xpm = 1, y = 1, yxy−1 = xp+1〉 (1) where p is an odd prime number and m > 1. We will show that Aut(P ) has a unique Sylow p-subgroup, Sp, and that in fact
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1993
ISSN: 0022-4049
DOI: 10.1016/0022-4049(93)90125-d