SMS scnews item created by Anthony Henderson at Tue 19 Feb 2008 1256
Type: Seminar
Distribution: World
Expiry: 29 Feb 2008
Calendar1: 29 Feb 2008 1205-1255
CalLoc1: Carslaw 373
CalTitle1: Algebra Seminar: Weigel -- Finite groups with minimal 1-PIM

Algebra Seminar

Finite groups with minimal 1-PIM

Thomas Weigel

29th February, 12:05-12:55pm, Carslaw 373


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.

After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

Anthony Henderson

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