School of Mathematics and Statistics
Algebra Seminar
The University of Sydney

University of Sydney Algebra Seminar


Thomas Weigel (University of Milan)

Friday 29th February, 12.05-12.55pm, Carslaw 373

Finite groups with minimal 1-PIM

Let G be a finite group, and let p be a divisor of the order of G. The dimension of P1 - the indecomposable projective F[G]-module with the trivial module in its head - is a multiple - say cp(G) - of the maximal p-power dividing the order of G. If G is p-soluble, this value is 1. However, in general the value of cp(G) is quite mysterious.

Together with G. Malle we have classified all finite simple groups G and prime numbers p for which cp(G) equals 1. Further analysis shows that for p in {2,3,5} a finite group G satisfying cp(G)=1 must be p-soluble.