A generalization of the Busemann-Petty problem on sections of convex bodies

It is proved that for arbitrarymεℕ and for a sufficiently nontrivial compact groupG of operators acting on a “typical”n-dimensional quotientX _n ofl ₁ ^m withm=(1+δ)n, there is a constantc=c(δ) such that Supported in part by KBN grant no. 2 P03A 034 10.