The Fixity of Groups of Prime-Power Order
M. F. Newman, Eamonn A. O’Brien, Aner Shalev · Bulletin of the London Mathematical Society · 1995
It is well known that the only groups of prime-power order which can act fixed point freely on a complex linear space are the cyclic or generalised quaternion groups. Given a positive integer f and a prime p exceeding f, we determine the p-groups which have a faithful complex representation such that the dimensions of the spaces of fixed points of non-trivial elements are at most f.