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.

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