Take the 2-minute tour ×  Let K be a finite field and let R,P be
groups (with R a subgroup of P). I know that the irreducible KP-
modules have dimensions 1,4 and 16 over K. I have a KP-module M,
and I know that M has dimension at most 5 over K. I also know
that M does not have a quotient of dimension 1 over K. Moreover,
if I consider M as a module over KR, it has a 2-dimensional
irreducible module. Is it necessarily the case that M is a
4-dimensional irreducible module over KP? (my initial reasoning
can be found in a comment below)  share|improve this question
The answer is no if and only if $\operatorname{Ext}^1(4,1)\neq
0$ in the obvious notation. If you said what P and R are maybe
someone could work it out, but a priori it is not even obvious
groups with these properties exist. –  m_t Feb 14 '12 at 14:02
Sorry, P and R are parabolic subgroups of the McLaughlin Group
in a minimal parabolic system. –  dward1996 Feb 14 '12 at 15:10
I think your answer has also proved that irrespective of the
answer to the ques