Alternate modules are subsymplectic
In this paper, an alternate module $(A,ϕ)$ is a finite abelian group $A$ with a $\mathbb{Z}$-bilinear application $ϕ:A\times A\rightarrow \mathbb{Q}/\mathbb{Z}$ which is alternate (i.e. zero on the diagonal). We shall prove that any alternate module is subsymplectic, i.e. if $(A,ϕ)$ has a Lagrangian of cardinal $n$ then there exists an abelian group $B$ of order $n$ such that $(A,ϕ)$ is a submodule of the standard symplectic module $B\times B^*$.
math.GR↗