Hyperbolic modules and cyclic subgroups

Maria Loukaki

Hyperbolic modules and cyclic subgroups

Group Theory 2022-06-22 v1

Authors: Maria Loukaki

Abstract

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 $G$ .

Keywords

hyperbolic groups hyperbolic geometry finite group theory

Cite

@article{arxiv.math/0412384,
  title  = {Hyperbolic modules and cyclic subgroups},
  author = {Maria Loukaki},
  journal= {arXiv preprint arXiv:math/0412384},
  year   = {2022}
}

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