کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4588051 1334170 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the sources of simple modules in nilpotent blocks
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the sources of simple modules in nilpotent blocks
چکیده انگلیسی

Let G be a finite group and let k be an algebraically closed field of characteristic p. If b is a nilpotent block of kG with defect group P, then there is a unique isomorphism class of simple kGb-modules and Puig proved that the source of this module is an endo-permutation kP-module. It is conjectured that the image of this source is always torsion in the Dade group.Let H be a finite group and let P be a p-subgroup of Aut(H). Also let c be a defect zero block of kH. If c is P-stable and BrP(c)≠0, then c is a nilpotent block of k(H⋊P) and k(H⋊P)c has P as a defect group. In this paper, we will investigate the sources of the simple k(H⋊P)c-modules when P≅Cp×Cp. Suppose that we can find an H and c as above such that a source of a simple k(H⋊P)c-module is not torsion in the Dade group. Then we can find H and c as above with H a central p′-extension of a simple group. When p⩾3 we show that H can be found in a quite restrictive subset of simple groups.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 319, Issue 11, 1 June 2008, Pages 4559-4574