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• W2811501997 abstract "Let K be a number field, let A be a finite dimensional semisimple K-algebra and let Lambda be an O_K-order in A. It was shown in previous work that, under certain hypotheses on A, there exists an algorithm that for a given (left) Lambda-lattice X either computes a free basis of X over Lambda or shows that X is not free over Lambda. In the present article, we generalise this by showing that, under weaker hypotheses on A, there exists an algorithm that for two given Lambda-lattices X and Y either computes an isomorphism X -> Y or determines that X and Y are not isomorphic. The algorithm is implemented in Magma for A=Q[G], Lambda=Z[G] and Lambda-lattices X and Y contained in Q[G], where G is a finite group satisfying certain hypotheses. This is used to investigate the Galois module structure of rings of integers and ambiguous ideals of tamely ramified Galois extensions of Q with Galois group isomorphic to Q_8 x C_2, the direct product of the quaternion group of order 8 and the cyclic group of order 2." @default.
• W2811501997 created "2018-07-10" @default.
• W2811501997 creator A5000020334 @default.
• W2811501997 creator A5090132590 @default.
• W2811501997 date "2018-06-22" @default.
• W2811501997 modified "2023-09-27" @default.
• W2811501997 title "Computing isomorphisms between lattices" @default.
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• W2811501997 hasPublicationYear "2018" @default.
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