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SUMMARY:The Loewy structures of the principal indecomposable modules (PIM'
 s) for small alternating groups in characteristic 2 and 3 - Ha Thu Nguyen
DTSTART:20140117T153000Z
DTEND:20140117T163000Z
UID:TALK50287@talks.cam.ac.uk
CONTACT:Julian Brough
DESCRIPTION:Let G be a finite group\, k be an algebraically closed field. 
 It is\nwell-known that when char k does not divide |G|\, every finite\ndim
 ensional kG-module is semisimple. However\, this is not the case if\nchar 
 k divides |G|. Nevertheless\, in this case\, we can visualize any\nfinite 
 dimensional kG-module as made up of many semisimple layers via\nits Loewy/
 socle series. In this talk\, we will give a quick review on\nvarious ways 
 of describing the structure of the PIM's of a finite group\nalgebra\, incl
 uding their module diagrams\, and the deep and beautiful\nresults on the s
 tructures of the PIM's in blocks with cyclic defects. We\nwill then work o
 ut the explicit Loewy structures of the principal\nindecomposable modules 
 (PIM's) for A_6\, A_7\, A_8\, and A_9 in\ncharacteristic 3\, and if time p
 ermits\, in characteristic 2.
LOCATION:CMS\, MR5
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