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The non‐projective part of the tensor powers of a module

Let M be a finite‐dimensional modular representation of a finite group G . We consider the dimensions of the non‐projective part of the tensor powers M⊗n of M , and we write γG(M) for the lim sup of their n th roots. We investigate the properties of the invariant γG(M) , using tools from representation theory, and from the theory of commutative Banach algebras.