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...

A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal deformations sending the standard flat torsion-free quaternionic contac...

In a pointed category with kernels and cokernels, we characterize torsion–free classes in terms of their closure under extensions. They are also described as indexed reflections. We obtain a corresponding characterization of torsion classes by formal categorical dualization.

The study of modules over a finite von Neumann algebra A can be advanced by the use of torsion theories. In this work, some torsion theories for A are presented, compared and studied. In particular, we prove that the torsion theory (T,P) (in which a module is torsion if it is zero-dimensional) is equal to both Lambek and Goldie torsion theories for A. Using torsion theories, we describe the inj...

In recent years, the RFRS condition has been used to analyze virtual fibering in 3-manifold topology. Agol’s work shows that any 3-manifold with zero Euler characteristic satisfying the RFRS condition on its fundamental group virtually fibers over the circle. In this note we will show that a finitely generated nilpotent group is either virtually abelian or is not virtually RFRS. As a corollary,...

Fix integers r, k, g with r > k > 0 and g ≥ 2. Let X be an integral projective curve with g := pa(X) and E a rank r torsion free sheaf on X which is a flat limit of a family of locally free sheaves on X. Here we prove the existence of a rank k subsheaf A of E such that r(deg(A)) ≥ k(deg(E)) − k(r − k)g. We show that for every g ≥ 9 there is an integral projective curve X,X not Gorenstein, and a...

An ideal I in a Noetherian ringR is normally torsion-free if Ass(R/I) = Ass(R/I) for all t ≥ 1. We develop a technique to inductively study normally torsion-free square-free monomial ideals. In particular, we show that if a squarefree monomial ideal I is minimally not normally torsion-free then the least power t such that I has embedded primes is bigger than β1, where β1 is the monomial grade o...

We show some mathematical links between partially observable (PO) games in which information is regularly revealed, and simultaneous actions games. Using this, we study the extension of Monte-Carlo Tree Search algorithms to PO games and to games with simultaneous actions. We apply the results to Urban Rivals, a free PO internet card game with more than 10 millions of registered users.

We prove a Freiheitssatz for one-relator products of torsion-free groups, where the relator has syllable length at most [Formula: see text]. This result applications to equations over groups: in particular singular equation text] group solution some overgroup.