# A Phan-type theorem for orthgonal [sic] groups [electronic resource] /

Abstract (Summary)

Corneliu Hoffman, Advisor
Phan’s theorem and the Curtis-Tits’ theorem are useful tools in the original proof of
the Classification of Finite Simple Groups and the ongoing Gorenstein-Lyons-Solomon
revision. Bennett, Gramlich, Hoffman and Shpectorov proved in a series of papers that
Phan’s theorem and the Curtis-Tits’ theorem were results with very geometric proofs.
They created a technique to prove these results which was generalized to produce what
they called Curtis-Phan-Tits Theory. The present paper applies this technique to the
orthogonal groups. A geometry is created on which a particular orthogonal group acts
flag-transitively. The geometry is shown to be both connected and then simply connected
when the dimension of the orthgonal group is at least five (except when the field is
order three). After these facts are established Tits’ lemma is used to conclude that the
orthogonal group is the universal completion of an interesting amalgam of subgroups that
is associated with the geometry. This type of result is useful in the context of identifying
a group when there is knowledge of the subgroup structure.
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Bibliographical Information:

Advisor:

School:Bowling Green State University

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:orthogonalization methods finite groups

ISBN:

Date of Publication: