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Canonical factorisability and a variant of Martinet’s conjecture. (English) Zbl 0751.11053
With Galois module theory as the background and the motivation arithmetical, the concept of factorisability has been studied in a representation-theoretic setting in the context of arbitrary finite groups, and more recently by means of certain derived equivalence relations between lattices over abelian group rings. The author of this paper deals with Fröhlich’s canonical factor equivalence showing its arithmetical interest, as well as giving explicit new results on Martinet’s conjecture (including a negative answer to a variant of the conjecture posed recently by M. J. Taylor).

MSC:
11R32 Galois theory
11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers
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