Let the finite group A be acting on a finite group G
with ([mid ]A[mid ], [mid ]G[mid ])=1. Let Γ be the
of A and G. Let χ be a character of Γ irreducible
after restriction to G. In a previous paper by Brian Hartley
and the author, we proved that the restriction of χ to S
belongs to the set [Cscr ](S) obtained by running
over all χ that arise in this manner, by assuming, in addition, that
G is a product of extraspecial groups.
This was proved in general, assuming only some condition on the Green
functions of groups of Lie type
that is not as yet fully verified. In the present paper, we define the map
Q(χ): S[map ][Copf ] by
=[mid ]CG(s)[mid ]/χ(s).
We prove that Q(χ)∈[Cscr ](S) under the same hypotheses.
In particular, the character quotient
Q(χ) is an ordinary character.