Counterexamples to a fiber theorem

We exhibit a counterexample to a fiber theorem stated by F. Fumagalli [J. Algebra 283 (2) (2005), 639-654] and show how it affects the rest of Fumagalli's paper. As a consequence, whether the poset A_p(G) is homotopy equivalent to a wedge of spheres for any finite solvable group G seems to remain an open question

Elementary abelian subgroups in p-groups of class 2

All the results in this work concern (finite) p-groups. Chapter 1 is concerned with classifications of some classes of p-groups of class 2 and there are no particularly new results in this chapter, which serves more as an introductory chapter. The "geometric" method we use for these classifications differs however from the standard approach, especially for p-groups of class 2 with cyclic center, and can be of some interest in this situation. This "geometry" will for instance, prove to be particularly useful for the description of the automorphism groups performed in Chapter 3. Our main results can be found in chapters 2 and Chapter 3. The results of Chapter 2 have a geometric flavour and concern the study of upper intervals in the poset Ap(P) for p-groups P. We already know from work of Bouc and Thévenaz [8], that Ap(P)≥2 is always homotopy equivalent to a wedge of spheres. The first main result in Section 2.4, is a sharp upper bound, depending only on the order of the group, to the dimension of the spheres occurring in Ap(P)≥2. More precisely, we show that if P has order pn, then H~k(Ap(P)≥2) = 0 if k ≥ ⎣n-1/2⎦. The second main result in this section is a characterization of the p-groups for which this bound is reached. The main results in Section 2.3 are numerical values for the number of the spheres occurring in Ap(P)≥2 and their dimension, when P is a p-group with a cyclic derived subgroup. Using these calculations, we determine precisely in Section 2.5, for which p-groups with a cyclic center, the poset Ap(P) is homotopically Cohen-Macaulay. Section 2.7 is an attempt to generalize the work of Bouc and Thévenaz [8]. The main result of this section is a spectral sequence E1rs converging to H~r+s(Ap(P)>Z), for any Z ∈ Ap(P). We show also that this spectral sequence can be used to recover Bouc and Thévenaz's results [8]. In Section 2.8, we give counterexamples to results of Fumagalli [12]. As an important consequence, Fumagalli's claim that Ap(G) is homotopy equivalent to a wedge of spheres, for solvable groups G, seems to remain an open question. The results of Chapter 3 are more algebraic and concern automorphism groups of p-groups. The main result is a description of Aut(P), when P is any group in one of the following two classes: p-groups with a cyclic Frattini subgroup. odd order p-groups of class 2 such that the quotient by the center is homocyclic

Philippe Claudel’s Brodeck as a parody of the fable or the Holocaust universalized

This article examines Philippe Claudel’s 2007 novel Brodeck (French title: Le Rapport de Brodeck) that allegorizes the Holocaust by parodying tropes and narrative structures characteristic to fairy tales and fables. While analyzing the author’s simultaneous inscription and subversion of the two ancient genres, I speculate about the possible reasons for his narrative choices and consider the meanings generated by his indirect representation of the Nazi genocide. Considering the widespread view of the Holocaust as sacred and unique, the article problematizes the novel’s universalization of the Jewish tragedy, which Claudel achieves by drawing on genres shunning historical and geographical specificity, and aiming to convey timeless and universal truths

Elementary abelian subgroups in p-groups with a cyclic derived subgroup

AbstractLet p be an arbitrary prime number and let P be a finite p-group. Let Ap(P) be the partially ordered set (poset for short) of all non-trivial elementary abelian subgroups of P ordered by inclusion and let Ap(P)⩾2 be the poset of all elementary abelian subgroups of P of rank at least 2. In [Serge Bouc, Jacques Thévenaz, The poset of elementary abelian subgroups of rank at least 2, Monogr. Enseign. Math. 40 (2008) 41–45], Bouc and Thévenaz proved that Ap(P)⩾2 has the homotopy type of a wedge of spheres (of possibly different dimensions). The general objective of this paper is to obtain more refined information on the homotopy type of the posets Ap(P) and Ap(P)⩾2. We give three different kinds of results in this direction.Firstly, we compute exactly the homotopy type of Ap(P)⩾2 when P is a p-group with a cyclic derived subgroup, that is we give the number of spheres occurring in each dimension in Ap(P)⩾2.Secondly, we compute a sharp upper bound on the dimension of the spheres occurring in Ap(P)⩾2 and give information on the p-groups for which this bound is reached.Thirdly, we determine explicitly for which of the p-groups with a cyclic derived subgroup the poset Ap(P) is homotopically Cohen–Macaulay

Counterexamples to a fiber theorem

AbstractWe exhibit a counterexample to a fiber theorem stated by F. Fumagalli in [Francesco Fumagalli, On the homotopy type of the Quillen complex of finite soluble groups, J. Algebra 283 (2) (2005) 639–654] and show how it affects the rest of Fumagalli's paper. As a consequence, whether the poset Ap(G) is homotopy equivalent to a wedge of spheres for any finite solvable group G seems to remain an open question

Approche pédologique du milieu prairial en Margeride

International audienc

Three cases of BRAF mutation negative Erdheim-Chester disease with a challenging distinction from IgG4-related disease

Erdheim-Chester disease (ECD) is a rare non-Langerhans histiocytosis with slow progression over the years that is particularly difficult to diagnose

Three cases of BRAF mutation negative Erdheim-Chester disease with a challenging distinction from IgG4-related disease

Abstract Background Erdheim-Chester disease (ECD) is a rare non-Langerhans histiocytosis with slow progression over the years that is particularly difficult to diagnose. Cases Here we report three cases of ECD without BRAF mutation presenting with a renal mass, hairy kidney appearance, and a rather benign course, for which the diagnosis of ECD was delayed, characterized by multiple investigations and unsuccessful treatments attempts. In two cases the distinction from IgG4-related disease required multiple investigations and reevaluation of the clinical, radiological, histological, and immunological characteristics. Conclusion A correct diagnosis of ECD may take several years and often requires revisiting previous hypotheses. Reassessment of histological slides and more modern complementary exams such as PET-CT or BRAF and MAPK-ERK mutation analysis can help to confirm the diagnosis of ECD and to select effective therapy. </jats:sec

ABC des polypes coliques [Abecedary of colonic polyps]

Colonic polyps are very common in the general population. Some polyps present a cancerization risk and their screening and management by endoscopy reduce the risk of colorectal cancer. Other polyps do not need specific follow-up. There are different types of polyps whose classification has been updated over the last ten years. Serrated polyps now intersect hyperplastic polyps, sessile serrated adenomas and traditional serrated adenomas. Current recommendations are to resect and histologically analyze each colonic polyp to define a personalized endoscopic surveillance strategy. Some colonic polyposis syndromes require management in a specialized center