Abstract
Partly because in the definition of a symplectic amalgam (see Definition 1.2) we have L 1/O p (L 1) ≅ SL2(q), the group SL 2(q) and its GF(p)-modules play a pivotal role in the exploration of these amalgams. For this chapter we fix q = p a, k = GF(q) and X = SL2(q). The chapter is divided into two sections. The first section deals with the subgroup structure and covering groups of X. These results are for the most part well-known and good sources are [61] and [79]. The second section is devoted to kX-modules and we begin by presenting a description of all irreducible kX-modules as given by Brauer and Nesbitt in [22]. Then, using results on generation of X by p-elements, we characterize those GF(p)X-modules that have small order. We further determine the GF(p)X-modules on which a Sylowp-subgroup ofX can operate quadratically. The chapter closes with a module result for SL2(2) ≀ 2
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© 2002 Springer-Verlag London
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Parker, C., Rowley, P. (2002). The Structure of SL2(q) and its Modules. In: Symplectic Amalgams. Springer Monographs in Mathematics. Springer, London. https://doi.org/10.1007/978-1-4471-0165-9_3
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DOI: https://doi.org/10.1007/978-1-4471-0165-9_3
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1088-0
Online ISBN: 978-1-4471-0165-9
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