Integral and p-modular semisimple deformations for p-solvable groups of finite representation type

FINITE p-GROUPS IN REPRESENTATION THEORY

Semisimple characters for p-adic classical groups

Let G be a unitary, symplectic or orthogonal group over a non-archimedean local field of residual characteristic different from 2, considered as the fixed point subgroup in a general linear group G̃ of an involution. Following [7] and [13], we generalize the notion of a semisimple character for G̃ and for G. In particular, following the formalism of [4], we show that these semisimple characters h...

Tits p-indexes of semisimple algebraic groups

The first author has recently shown that semisimple algebraic groups are classified up to motivic equivalence by the local versions of the classical Tits indexes over field extensions, known as Tits p-indexes. We provide in this article the complete description of the values of the Tits p-indexes over fields. From this exhaustive study, we also deduce criteria for motivic equivalence of semisim...

ENDOTRIVIAL MODULES FOR p-SOLVABLE GROUPS

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.

Finite $p$-groups and centralizers of non-cyclic abelian subgroups

A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is ‎cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq‎ ‎Z(G)$‎. ‎In this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{CAC}$-$p$-groups‎.