Serre homotopy theory in subcategories of simplicial groups

If S subset of or equal to Z is a multiplicative system and C is the class of the S-torsion abelian groups, we study Serre mod C homotopy theory in th e subcategories of simplicial groups whose objects have trivial Moore compl ex in dimensions less than r and greater than n for 0 less than or equal to r less than or equal to n. This is carried by giving a closed model struct ure in these categories and then studying the associated homotopy theory. W hen n --> infinity we obtain the Serre homotopy theory for r-reduced simpli cial groups studied by Quillen in Arm. Math. 90 (1969) 205-295. If S = Z - {0} and r = 1 we have the corresponding rational homotopy theory. The case n = r + 1 allows to consider Serre homotopy theory in categories of cat-gro ups or crossed modules of groups. (C) 2000 Elsevier Science B.V. All rights reserved, MSC. 18G30; 55P62; 55U35.