Maria Loukaki
Published 2004-12-19Version 1
Let $G$ be a finite group of odd order, $\F$ a finite field of odd characteristic $p$ and $\B$ a finite--dimensional symplectic $\F G$-module. We show that $\B$ is $\F G$-hyperbolic, i.e., it contains a self--perpendicular $\F G$-submodule, iff it is $\F N$-hyperbolic for every cyclic subgroup $N$ of $G$.
A characterization of certain finite groups of odd order
On partial $Π$-property of subgroups of finite groups
On the number of cyclic subgroup in finite groups
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