eTheses Repository

# Overgroups of a linear Singer cycle in classical groups

Brookfield, Tom (2015)
Ph.D. thesis, University of Birmingham.

 PDF (701Kb)Accepted Version

## Abstract

There are well known embeddings of GL$$_n$$ ($$q$$) in Sp$$_2$$$$_n$$ ($$q$$) and GO+$$_2$$$$_n$$ ($$q$$), as well as an embedding of GL$$_n$$ ($$q$$$$^2$$) in GU$$_2$$$$_n$$ ($$q$$). These give embeddings of Singer cycles of GL$$_n$$ ($$q$$) and GL$$_n$$ ($$q$$$$^2$$) in the corresponding classical group, which we call $$linear$$ $$Singer$$ $$cycles$$. In this thesis, we classify the overgroups of such a Singer cycle in these groups.

Type of Work: Ph.D. thesis. Parker, Christopher Colleges (2008 onwards) > College of Engineering & Physical Sciences School of Mathematics QA Mathematics University of Birmingham 5972
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.

Repository Staff Only: item control page