caa a22 4500 475738144 CHVBK 20180406123452.0 cr unu---uuuuu 170329e20000201xx s 000 0 eng 10.1007/s002229900026 doi (NATIONALLICENCE)springer-10.1007/s002229900026 The group of endo-permutation modules [Elektronische Daten] [Serge Bouc, Jacques Thévenaz] Abstract. : The group D(P) of all endo-permutation modules for a finite p-group P is a finitely generated abelian group. We prove that its torsion-free rank is equal to the number of conjugacy classes of non-cyclic subgroups of P. We also obtain partial results on its torsion subgroup. We determine next the structure of ℚ⊗D(-) viewed as a functor, which turns out to be a simple functor S E, ℚ, indexed by the elementary group E of order p 2 and the trivial Out(E)-module ℚ. Finally we describe a rather strange exact sequence relating ℚ⊗D(P), ℚ⊗B(P), and ℚ⊗R(P), where B(P) is the Burnside ring and R(P) is the Grothendieck ring of ℚP-modules. Springer-Verlag Berlin Heidelberg, 2000 Bouc Serge UFR de Mathématiques, Université de Paris VII, 2 place Jussieu, F-75251 Paris, France (e-mail: bouc@math.jussieu.fr), France aut Thévenaz Jacques Institut de Mathématiques, Université de Lausanne, CH-1015 Lausanne, Switzerland (e-mail: Jacques.Thevenaz@ima.unil.ch), Switzerland aut Inventiones mathematicae Springer Berlin Heidelberg 139/2(2000-02-01), 275-349 0020-9910 139:2<275 2000 139 222 https://doi.org/10.1007/s002229900026 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002229900026 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bouc Serge UFR de Mathématiques, Université de Paris VII, 2 place Jussieu, F-75251 Paris, France (e-mail: bouc@math.jussieu.fr), France aut NATIONALLICENCE 700 1- Thévenaz Jacques Institut de Mathématiques, Université de Lausanne, CH-1015 Lausanne, Switzerland (e-mail: Jacques.Thevenaz@ima.unil.ch), Switzerland aut NATIONALLICENCE 773 0- Inventiones mathematicae Springer Berlin Heidelberg 139/2(2000-02-01), 275-349 0020-9910 139:2<275 2000 139 222 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer