ENDOTRIVIAL MODULES FOR p-SOLVABLE GROUPS
نویسنده
چکیده
We determine the torsion subgroup of the group of endotrivial modules for a finite solvable group in characteristic p. We also prove that our result would hold for p-solvable groups, provided a conjecture can be proved about the case of p-nilpotent groups.
منابع مشابه
The Group of Endotrivial Modules for the Symmetric and Alternating Groups
We complete a classification of the groups of endotrivial modules for the modular group algebras of symmetric groups and alternating groups. We show that, for n p2, the torsion subgroup of the group of endotrivial modules for the symmetric groups is generated by the sign representation. The torsion subgroup is trivial for the alternating groups. The torsion-free part of the group is free abelia...
متن کاملEndotrivial Modules over Groups with Quaternion or Semi-dihedral Sylow 2-subgroup
Suppose that G is a finite group and that k is a field of characteristic p. Endotrivial kG-modules appear in a natural way in many areas surrounding local analysis of finite groups. They were introduced by Dade [14] who classified them in the case that G is an abelian p-group. A complete classification of endotrivial modules over the modular group rings of p-groups was completed just a few year...
متن کاملEndotrivial Modules in the Cyclic Case
The purpose of this note is to determine all endotrivial modules in prime characteristic p, for a finite group having a cyclic Sylow p-subgroup. In other words, we describe completely the group of endotrivial modules in that case. The endotrivial modules are a family of finitely generated modules for a group algebra of a finite group which appear naturally in modular representation theory. Seve...
متن کاملThe Torsion Group of Endotrivial Modules
Let G be a finite group and let T (G) be the abelian group of equivalence classes of endotrivial kG-modules, where k is an algebraically closed field of characteristic p. We determine, in terms of the structure of G, the kernel of the restriction map from T (G) to T (S), where S is a Sylow p-subgroup of G, in the case when S is abelian. This provides a classification of all torsion endotrivial ...
متن کاملNotes from a problem session on support varieties
For groups other than p-groups, some work has been done for general situations [12, 13] and for simple groups [4, 5, 6]. Balmer [2] has made connections with the Picard group of the spectrum of the stable category. Nakano and the author have had some success extending the results to more general finite group schemes. For example, in the case of a p-restricted Lie algebra whose cohomology ring s...
متن کامل