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Reality and Strong Reality in Finite Symplectic Groups

Schrandt, Spencer
Abstract
When an element of a given group lies in the same conjugacy class as its inverse element, it is said to be real, and a conjugacy class with one real element must have all of its other elements real as well, so such a class is itself called real. In addition, a real element is called strongly real if the element which conjugates it to its inverse can be taken to be an involution, that is, an element whose square is the identity. We investigate the concepts of reality and strong reality in symplectic groups over a finite field, which have implications to conjectures on the representations of finite groups. In particular, we present progress in the direction of showing that all real classes of the projective symplectic group over a field of order q are strongly real.
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2021-05-01
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Undergraduate Honors Theses
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Vinroot, C. Ryan
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Mathematics
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https://scholarworks.wm.edu/handle/internal/11122
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