# Overgroups of a linear Singer cycle in classical groups

Brookfield, Tom (2015). Overgroups of a linear Singer cycle in classical groups. University of Birmingham. Ph.D.

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## 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: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Parker, ChristopherUNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: Engineering and Physical Sciences Research Council
Subjects: Q Science > QA Mathematics
URI: http://etheses.bham.ac.uk/id/eprint/5972

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