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Journal of the London Mathematical Society 2006 73(1):126-140; doi:10.1112/S0024610705022386
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© The London Mathematical Society

On the Reduced Lefschetz Module and the Centric p-Radical Subgroups II

Masato Sawabe

Department of Mathematics, Naruto University of Education Naruto, Tokushima 772-8502, Japan sawabe{at}naruto-u.ac.jp

Received 26 October 2004. Revision received 13 June 2005.

In this paper, we give a lower bound of the p-part of the reduced Euler characteristic of the order complex of the centric p-radical subgroups by studying vertices of indecomposable summands of the reduced Lefschetz module. This bound is in fact best possible for at least some groups, and also provides a uniform explanation of the observed phenomenon on the reduced Euler characteristic for some sporadic simple groups.


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