Abstract.
Let F be a field and, for i = 1,2, let G i be a group and V i an irreducible, primitive, finite dimensional FG i -module. Set G = G 1 \times G 2 and \(V=V_1\otimes _F V_2\). The main aim of this paper is to determine sufficient conditions for V to be primitive as a G-module. In particular this turns out to be the case if V 1 and V 2 are absolutely irreducible and V 1 is absolutely quasi-primitive. Thus we extend a result of N.S. Heckster, who has shown that V is primitive whenever G is finite and F is the complex field. We also give a characterization of absolutely quasi-primitive modules. Ultimately, our results rely on the classification of finite simple groups.
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Received: 25.10.1999
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Lucchini, A., Tamburini, M. Tensor products of primitive modules. Arch. Math. 77, 149–154 (2001). https://doi.org/10.1007/PL00000474
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DOI: https://doi.org/10.1007/PL00000474