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Person# Nadia Mazza

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Finite group

In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just

Abelian group

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are

Coxeter group

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors). Indeed, the finite Coxeter gr

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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 investigate the torsion-free part TF(G) of the group T(G) and look for generators of TF(G). We describe three methods for obtaining generators. Each of them only gives partial answers to the question but we obtain more precise results in some specific cases. We also conjecture that TF(G) can be generated by modules belonging to the principal block and we prove the conjecture in some cases.

Let G be a finite group with a Sylow 2-subgroup P which is either quaternion or semi-dihedral. Let k be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial kG-modules, whose restrictions to P are isomorphic to the direct sum of the known exotic endotrivial kP-modules and some projective modules. This provides a description of the group T(G) of endotrivial kG-modules.

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.

2011