Endomorphism algebras of transitive permutation modules for p -groups

Author： Towers Matthew  

Publisher： Springer Publishing Company

ISSN： 0003-889X

Source： Archiv der Mathematik, Vol.92, Iss.3, 2009-03, pp. : 215-227

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Abstract

Let G be a finite p-group with subgroup H and k a field of characteristic p. We study the endomorphism algebra E = EndkG(kH ↑G), showing that it is a split extension of a nilpotent ideal by the group algebra kNG(H)/H. We identify the space of endomorphisms that factor through a projective kG-module and hence the endomorphism ring of kH ↑G in the stable module category, and determine the Loewy structure of E when G has nilpotency class 2 and [G, H] is cyclic.

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