Thomas Weigel (University of Milan)
Friday 29th February, 12.05-12.55pm, Carslaw 373
Finite groups with minimal 1-PIMLet G be a finite group, and let p be a divisor of the order of G. The dimension of P_{1} - the indecomposable projective F[G]-module with the trivial module in its head - is a multiple - say c_{p}(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 c_{p}(G) is quite mysterious. Together with G. Malle we have classified all finite simple groups G and prime numbers p for which c_{p}(G) equals 1. Further analysis shows that for p in {2,3,5} a finite group G satisfying c_{p}(G)=1 must be p-soluble. |