Abstract
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 ( 2 m , F q ) , GO ( 2 m + 1 , F q ) , GO − ( 2 m , F q ) , GO + ( 2 m , F q ) or GU ( n , F q 2 ) . The algorithms described here are implemented in the Magma Computer Algebra System.
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