From: Bob OLIVER
Date: Tue, 7 Nov 2006 19:48:38 +0100 (CET)
Dear Neal,
The p-stubborn subgroups of U(n) are described in my paper in JPAA 92
(1994), 55-78. I think the p-stubborn/radical subgroups of symmetric
groups go back to Alperin-Fong; in any case I'm sure they were known long
before my paper.
I think this makes your other questions irrelevant; let me know if that's
not the case.
Bob
_________________________________________________________________
Subject: Response to Neil's question
From: Jesper Grodal
Date: Tue, 7 Nov 2006 16:42:34 -0600 (CST)
Dear Neil & others,
> 1) Am I right in thinking that one cannot just enumerate the (conjugacy
> classes of) p-stubborn subgroups of U(n)? If I understand correctly,
this
> includes the corresponding problem for the symmetric group, which seems
to
> be hard. (Of course, I am thinking of the case where n >= p.)
Bob Oliver enumerated the p-stubborn (aka p-radical) subgroups of U(n) in
"p-stubborn subgroups of classical compact Lie groups". J. Pure Appl.
Algebra 92 (1994), no. 1, 55--78.
The corresponding problem for symmetric groups is solved in: Alperin, J.
L.; Fong, P. "Weights for symmetric and general linear groups". J. Algebra
131 (1990), no. 1, 2--22.
The problem you might be remembering for symmetric groups could be the
problem of determining the homotopy type of the poset of p-radical
subgroups, which is not known for large n and appears to be complicated.
There exists a vast group theoretic litterature listing the p-radical
subgroups in different finite groups, to a large part motivated by their
appearance in the Alperin weight conjecture.
Jesper