, Volume 54, Issue 3, pp 266-290

Symplectic modules

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Abstract

A symplectic module is a finite group with a regular antisymmetric form. The paper determines sufficient conditions for the invariants of the maximal isotropic subgroups (Lagrangians), and asymptotic values for a lower bound of a group which contains Lagrangians of all symplectic modules of a fixed orderp n. These results have application to the splitting fields of universal division algebras.