The Loewy structures of the principal indecomposable modules (PIM's) for small alternating groups in characteristic 2 and 3
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 Ha Thu Nguyen
 Friday 17 January 2014, 15:3016:30
 CMS, MR5.
If you have a question about this talk, please contact Julian Brough.
Let G be a finite group, k be an algebraically closed field. It is
wellknown that when char k does not divide G, every finite
dimensional kGmodule is semisimple. However, this is not the case if
char k divides G. Nevertheless, in this case, we can visualize any
finite dimensional kGmodule as made up of many semisimple layers via
its Loewy/socle series. In this talk, we will give a quick review on
various ways of describing the structure of the PIM ’s of a finite group
algebra, including their module diagrams, and the deep and beautiful
results on the structures of the PIM ’s in blocks with cyclic defects. We
will then work out the explicit Loewy structures of the principal
indecomposable modules (PIM’s) for A_6, A_7, A_8, and A_9 in
characteristic 3, and if time permits, in characteristic 2.
This talk is part of the Junior Algebra and Number Theory seminar series.
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