Induction from Elementary Abelian Subgroups
نویسندگان
چکیده
منابع مشابه
Norm formulas for finite groups and induction from elementary abelian subgroups
It is known that the norm map NG for a finite group G acting on a ring R is surjective if and only if for every elementary abelian subgroup E of G the norm map NE for E is surjective. Equivalently, there exists an element xG ∈ R with NG(xG) = 1 if and only for every elementary abelian subgroup E there exists an element xE ∈ R such that NE(xE) = 1. When the ring R is noncommutative, it is an ope...
متن کاملThe Poset of Elementary Abelian Subgroups Of
If p is a prime number, the poset of all nontrivial elementary abelian p -subgroups of a finite group plays an important role in both group theory and representation theory. It was studied by Quillen [9], who proved among many other things that it is homotopy equivalent to the poset of all nontrivial p -subgroups. In the case of a p -group P , one might believe that this poset has no interest s...
متن کاملElementary Abelian Subgroups in p - Groups of Class 2 THÈSE
All the results in this work concern (finite) p-groups. Chapter 1 is concerned with classifications of some classes of p-groups of class 2 and there are no particularly new results in this chapter, which serves more as an introductory chapter. The “geometric” method we use for these classifications differs however from the standard approach, especially for p-groups of class 2 with cyclic center...
متن کاملp-GROUPS WITH MAXIMAL ELEMENTARY ABELIAN SUBGROUPS OF RANK 2
Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2. It follows that if G has rank greater than p, then the poset E(G) of elementary abelian subgroups of G of rank at least 2 is connected and the torsion-free rank of the group of endotrivial kG-modules is one, for any field k of charac...
متن کاملTHE NUMBER OF CHAINS OF SUBGROUPS OF A FINITE ELEMENTARY ABELIAN p-GROUP
The starting point for our discussion is given by the paper [5], where a formula for the number of rooted chains of subgroups of a finite cyclic group is obtained. This leads in [3] to precise expression of the well-known central Delannoy numbers in an arbitrary dimension and has been simplified in [2]. Some steps in order to determine the number of rooted chains of subgroups of a finite elemen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1996
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0026