Linearity of dimension functions for semilinear 𝐺-spheres

Abstract

In this paper, we show that the dimension function of every semilinear G G -sphere is equal to that of a linear G G -sphere for finite nilpotent groups G G of order p n q m p^nq^m , where p p , q q are primes. We also show that there exists a semilinear G G -sphere whose dimension function is not virtually linear for an arbitrary nonsolvable compact Lie group G G .