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 (mod2). 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 (mod2) 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.
