8 citations · 9 across the 12 of their papers we have counts for
16 papers
On the separability of some Green biset functors
Serge Bouc, Nadia Romero
We show that the Green biset functor of complex characters over , is not separable, i.e. it is not projective as a bimodule over itself. Also, we show…
Koszul resolution for linear monoidal functors
Serge Bouc, Nadia Romero
We introduce regular sequences and associated Koszul resolutions for monoids in the category of functors over an essentially small linear symmetric monoidal category. Next we defin…
Hochschild cohomology for functors on linear symmetric monoidal categories
Nadia Romero
Let be a commutative ring with unit. We develop a Hochschild cohomology theory in the category of linear functors defined from an essentially small symmetric mono…
On the essential algebra of the shifted Burnside biset functor
Nadia Romero
We describe the essential algebra, , of the Burnside biset functor shifted by a group , at a group , in two cases. First, when and are both finite…
Green fields
Serge Bouc, Nadia Romero
We introduce {\em Green fields}, as commutative Green biset functors with no non-trivial ideals. We state some of their properties and give examples of known Green biset functors w…
Shifted functors of linear representations are semisimple
Serge Bouc, Nadia Romero
We prove that, for any fields and of characteristic and any finite group , the category of modules over the shifted Green biset functor $(kR_{\mathbb{F}})_T…
Deflation and tensor induction on the Frobenius-Wielandt morphism
Nadia Romero
We explore conditions for the Frobenius-Wielandt morphism to commute with the operations of deflation and tensor induction on the Burnside ring. In doing this, we review the commut…
The center of a Green biset functor
Serge Bouc, Nadia Romero
For a Green biset functor , we define the commutant and the center of and we study some of their properties and their relationship. This leads in particular to the main appl…
The additive completion of the biset category
Jesús Ibarra, Alberto G. Raggi-Cárdenas, Nadia Romero
Let be a commutative unital ring. We construct a category of fractions , where is a finite group and is a finite -set, and with morphisms given…
The Whitehead group of (almost) extra-special p-groups with p odd
Serge Bouc, Nadia Romero
Let p be an odd prime number. We describe the Whitehead group of all extra-special and almost extra-special p-groups. For this we compute, for any finite p-group P , the subgroup C…
Cyclic cellularity and active sums
Nadia Romero
Let be a group and let be a family of subgroups of closed under conjugation. For a positive integer , let denote a cyclic group of order . We show…
Computing Whitehead groups using genetic bases
Nadia Romero
We combine results about Whitehead groups of finite groups with results about genetic bases of finite -groups to compute the Whitehead groups of some metacyclic -groups. Let…
Finite metacyclic groups as active sums of cyclic subgroups
Alejandro Díaz-Barriga, Francisco González-Acuña, Franciso Marmolejo +1
The notion of active sum provides an analogue for groups of that of direct sum for abelian groups. One natural question then is which groups are the active sum of cyclic subgroups.…
On fibred biset functors with fibres of order prime and four
Nadia Romero
This note has two purposes: First, to present a counterexample to a conjecture parametrizing the simple modules over Green biset functors, appearing in an author's previous article…
Simple modules over Green biset functors
Nadia Romero
We present three examples of Green biset functors for which their simple modules can be parametrized. These are particular cases of a conjecture by Serge Bouc classifying the simpl…
On primordial groups for the Green ring
Alberto Raggi-Cardenas, Nadia Romero
Consider the Mackey functor assigning to each finite group G the Green ring of finitely generated kG-modules, where k is a field of characteristic p>0. Thevenaz foresaw in 1988 tha…