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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机译：令G为有限的p群，其中子群H为子集，k为特征p的场。我们研究了内同构代数E = End kG （k H ↑ G ），表明它是幂等理想的分裂扩展。组代数kN G （H）/ H。我们确定了通过射影kG-模因分解的内同型空间，从而确定了稳定模块类别中k H ↑ G 的内同型环，并确定了Loewy结构。当G具有幂等等级2并且[G，H]是循环的时，E。
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