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On the structure of Generalized Symmetric Spaces of \bm{\mbox{SL}_{2}(\mathbb{F}_{\MakeLowercase{q}})}} and \bm{\mbox{GL}_{2}(\mathbb{F}_{\MakeLowercase{q}})}


Abstract


In this paper we will discuss the generalized symmetric spaces for \SL_2(\mathbb{F}_q) and \GL_2(\mathbb{F}_q). Specifically we will characterize the structure of these spaces and prove that when the characteristic of \mathbb{F}_q is not equal to two the extended generalized symmetric space is equal to the generalized symmetric space for \SL_2(\mathbb{F}_q) and nearly equal for \GL_2(\mathbb{F}_q) for all but one involution.

DOI Code: 10.1285/i15900932v37n2p1

Keywords: generalized symmetric space; special linear group; nite elds

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