G-Weights and p-Local Rank
Publish place: The Journal of Algebra and Related Topics، Vol: 5، Issue: 2
Publish Year: 1396
نوع سند: مقاله ژورنالی
زبان: English
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JR_JART-5-2_001
تاریخ نمایه سازی: 31 تیر 1403
Abstract:
Let k be field of characteristic p, andlet G be any finite group with splitting field k. Assume that B is a p-block of G.In this paper, we introduce the notion of radical B-chain C_{B}, and we show that the p-local rank of B is equals the length of C_{B}. Moreover, we prove that the vertex of a simple kG-module S is radical if and only if it has the same vertex of the unique direct summand, up to isomorphism, of the Sylow permutationmodule whose radical quotient is isomorphic to S. Finally, we prove the vertices of certain direct summands of the Sylow permutation module are bounds for the vertices of simple kG-modules.
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Authors
P. Manuel Dominguez Wade
Department of Mathematics, Matanzas University, Matanzas, Cuba