Concept

Rank of an abelian group

Related publications (24)

A sectional characterization of the Dade group

Let k be a field of characteristic p, let P be a finite p-group, where p is an odd prime, and let D(P) be the Dade group of endo-permutation kP-modules. It is known that D(P) is detected via deflation-restriction by the family of all sections of P which ar ...

2008

The classification of endo-trivial modules

Jacques Thévenaz

This paper settles the classification of all endo-trivial modules for a finite p-group, by treating the remaining case of a p-group having maximal elementary abelian subgroups of rank 2. It is shown that the modules constructed by Alperin using relative sy ...

2004

The group of endo-permutation modules

Jacques Thévenaz, Serge Bouc

The group D(P) of all endo-permutation modules for a finite p-group P is a finitely generated abelian group. We prove that its torsion-free rank is equal to the number of conjugacy classes of non-cyclic subgroups of P. We also obtain partial results on its ...

2000

Torsion endo-trivial modules

Jacques Thévenaz

We prove that the group T(G) of endo-trivial modules for a non-cyclic finite p-group G is detected on restriction to the family of subgroups which are either elementary abelian of rank 2 or (almost) extraspecial. This result is closely related to the probl ...

2000

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