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- JON F. CARLSON, NADIA MAZZA, DANIEL K. NAKANO
- 2007

- JON F. CARLSON, NADIA MAZZA, DANIEL K. NAKANO
- 2007

In this paper we determine the group of endotrivial modules for certain symmetric and alternating groups in characteristic p. If p = 2, then the group is generated by the class of Ω n (k) except in a few low degrees. If p > 2, then the group is only determined for degrees less than p 2. In these cases we show that there are several Young modules which are… (More)

- Serge Bouc, Nadia Mazza
- 2005

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 cohomolog-ical properties of the Tits building corresponding to the natural geometric structure of the lattice of subgroups of such p-groups.

We prove analogues of results of Glauberman and Thompson for fusion systems. Namely, given a (saturated) fusion system F on a finite p-group S, and in the cases where p is odd or F is S 4-free, we show that Z(N F (J(S))) = Z(F) (Glauberman), and that if C F (Z(S)) = N F (J(S)) = F S (S), then F = F S (S) (Thompson). As a corollary, we obtain a stronger form… (More)

The Dade group D(P) of a finite p-group P , formed by equivalence classes of endo-permutation 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 non-trivial element of its torsion subgroup D t (P) has order 2, (or also 4, in case p = 2).… (More)

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 p 2 , 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… (More)

- NADIA MAZZA, Jon Carlson, Daniel Nakano
- 2006

The group of endotrivial modules has recently been determined for a finite group having a normal Sylow p-subgroup. In this paper, we give and compare three different presentations of a torsion-free subgroup of maximal rank of the group of endotrivial modules. Finally, we illustrate the constructions in an example.

- Nadia Mazza
- 2005

The source of a simple kG-module, for a finite p-solvable group G and an algebraically closed field k of prime characteristic p, is an endo-permutation module (see [Pu1] or [Th]). L. Puig has proved, more precisely, that this source must be isomorphic to the cap of an endo-permutation module of the form Q/R∈S Ten P Q Inf Q Q/R (M Q/R), where M Q/R is an… (More)

We show that K∞ and K ∞ control transfer in every fusion system on a finite p-group when p ≥ 5, and that they control weak closure of elements in every fusion system on a finite p-group when p ≥ 3. This generalizes results of G. Glauberman concerning finite groups.