2012/06/30 by L. Puig, Lluis Puig, Puig, Lluis
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR
paper · pdf · doi:10.48550/arxiv.1207.0066
This paper is a corrected version of a previous preprint
openalex publication_date 2012/06/30 · arxiv created 2015/03/07 · arxiv updated 2015/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p be a prime, P a finite p-group and F a Frobenius P-category. The question on the existence of a suitable category Lsc extending the full subcategory of F over the set of F-selfcentralizing subgroups of P goes back to Dave Benson in 1994. In 2002 Carles Broto, Ran Levi and Bob Oliver formulate the existence and the uniqueness of the category Lsc in terms of the annulation of an obstruction 3-cohomology element and of the vanishing of a 2-cohomology group, and they state a sufficient condition for the vanishing of these n-cohomology groups. Recently, Amy Chermak has proved the existence and the uniqueness of Lsc via his objective partial groups, and Bob Oliver, following some of Chermak's methods, has also proved the vanishing of those n-cohomology groups for n > 1, both applying the Classification of the finite simple groups. Here we give direct proofs of the existence and the uniqueness of Lsc; moreover, in [11] we already show that Lsc can be completed in a suitable category L extending F and here we prove some functoriality of this correspondence.