Linearity of dimension functions for semilinear 𝐺-spheres

Nagasaki, Ikumitsu

doi:10.1090/S0002-9939-02-06512-7

Linearity of dimension functions for semilinear $G$-spheres
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Proc. Amer. Math. Soc. 130 (2002), 1843-1850 Request permission

Abstract:

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

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