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Constructive Sylow theorems for the classical groups

Academic Press Inc Elsevier Science
Publication Date
  • Qa Mathematics
  • Computer Science


Let r be a prime. We provide efficient algorithms to construct and solve the conjugacy problem for the Sylow r-subgroups of the classical groups over finite fields in their natural representations. We also provide algorithms to construct the normaliser of a Sylow r-subgroup of GL(n, F-q), Sp(2m, Fq), GO(2m + 1, Fq), GO(-) (2m, F-q), GO(+)(2m, F-q) or GU(n, F-q2). The algorithms described here are implemented in the MAGMA Computer Algebra System.

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