منابع مشابه
The Dade group of a metacyclic p-group
The Dade group D(P ) of a finite p-group P , formed by equivalence classes of endopermutation modules, is a finitely generated abelian group. Its torsion-free rank equals the number of conjugacy classes of non-cyclic subgroups of P and it is conjectured that every nontrivial element of its torsion subgroup D(P ) has order 2, (or also 4, in case p = 2). The group D(P ) is closely related to the ...
متن کاملON THE STRUCTURE OF THE AUTOMORPHISM GROUP OF A MINIMAL NONABELIAN p-GROUP (METACYCLIC CASE)
In this paper we find the complete structure for the automorphism groups of metacyclic minimal nonabelian 2-groups. This, together with [6, 7], gives the complete answer to the Question 15 from [5] (respectively Question 20 from [4]) in the case of metacyclic groups. We also correct some inaccuracies and extend the results from [13].
متن کاملThe Dade group of (almost) extraspecial p-groups
In this paper, we determine a presentation by explicit generators and relations for the Dade group of all (almost) extraspecial p-groups. The proof of the main result uses the cohomological properties of the Tits building corresponding to the natural geometric structure of the lattice of subgroups of such p-groups. AMS Subject Classification : 20C20, 20D15
متن کاملA sectional characterization of the Dade group
Let k be a field of characteristic p , let P be a finite pgroup, 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 are elementary abelian of rank ≤ 2. In this paper, we improve this result by characterizing D(P ) as the limit (with respect to deflation– r...
متن کاملBorel-smith Functions and the Dade Group
We show that there is an exact sequence of biset functors over p-groups 0 → Cb j −→B∗ Ψ −→D → 0 where Cb is the biset functor for the group of Borel-Smith functions, B ∗ is the dual of the Burnside ring functor, D is the functor for the subgroup of the Dade group generated by relative syzygies, and the natural transformation Ψ is the transformation recently introduced by the first author in [5]...
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: 2003
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00328-4