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Introduction

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Symplectic Amalgams

Part of the book series: Springer Monographs in Mathematics ((SMM))

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Abstract

From early work on finite permutation groups it became clear that group theory and arithmetic conditions were destined to be fellow travellers, Cauchy’s theorem [27] on the existence of elements of prime order being one such example. The advent of Sylow’s fundamental theorem [179] in 1872, intertwining prime numbers and group theoretic properties, set the seal on this alliance. The investigations by Galois into the minimal (non-trivial) permutation degree representations of L[in2}(p) (the 2-dimensional projective special linear group over GF(p), p a prime) revealed a further aspect. He showed that the minimum degree was p + 1 except when p ≤ 11 and then the minimum was p; this type of “small” case exceptions phenomena was to have many repercussions. (See, for example,[140, Chapter VII].)

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© 2002 Springer-Verlag London

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Parker, C., Rowley, P. (2002). Introduction. In: Symplectic Amalgams. Springer Monographs in Mathematics. Springer, London. https://doi.org/10.1007/978-1-4471-0165-9_1

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  • DOI: https://doi.org/10.1007/978-1-4471-0165-9_1

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1088-0

  • Online ISBN: 978-1-4471-0165-9

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