On diagonal entries of Cartan matrices of p-blocks

Abstract

In this short note, we show some inequalities on Cartan matrices, centers and socles of blocks of group algebras. Our main theorems are generalizations of the facts on dimension of Reynolds ideals.

arXiv comment4 pages, Changes from v1: Theorem1.1, Theorem1.2 and its proof, position of Corollary 3.4 in v1 (Corollary 3.2 in v2), some typos

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