The fixity of groups of prime-power order

M. F. Newman; E. A. O’Brien; Aner Shalev

doi:10.1112/blms/27.3.225

The fixity of groups of prime-power order

M. F. Newman, E. A. O’Brien, Aner Shalev

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	225-231
Number of pages	7
Journal	Bulletin of the London Mathematical Society
Volume	27
Issue number	3
DOIs	https://doi.org/10.1112/blms/27.3.225
State	Published - May 1995

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abstract = "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.",

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AB - 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.

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The fixity of groups of prime-power order

Abstract

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