Vol. 114, No. 2, 1984

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An Artin relation (mod 2) for finite group actions on spheres

Ronald Dotzel

Vol. 114 (1984), No. 2, 335–343
Abstract

Recently it has been shown that whenever a finite group G (not a p-group) acts on a homotopy sphere there is no general numerical relation which holds between the various formal dimensions of the fixed sets of p-subgroups (p dividing the order of G). However, if G is dihedral of order 2q (q an odd prime power) there is a numerical relation which holds (mod 2). In this paper, actions of groups G which are extensions of an odd order p-group by a cyclic 2-group are considered and a numerical relation (mod 2) is found to be satisfied (for such groups acting on spheres) between the various dimensions of fixed sets of certain subgroups; this relation generalises the classical Artin relation for dihedral actions on spheres.

Mathematical Subject Classification 2000
Primary: 57S17
Secondary: 57S25
Milestones
Received: 4 August 1982
Revised: 3 December 1982
Published: 1 October 1984
Authors
Ronald Dotzel