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Computing Hall subgroups of finite groups

Part of: Other groups of matrices Representation theory of groups Permutation groups Group theory and generalizations

Published online by Cambridge University Press:  01 August 2012

Bettina Eick  and
Alexander Hulpke
Bettina Eick
Affiliation:
Institut Computational Mathematics, TU Braunschweig, D-38106 Braunschweig, Germany (email: beick@tu-bs.de)
Alexander Hulpke
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA (email: hulpke@math.colostate.edu)

Abstract

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We describe an effective algorithm to compute a set of representatives for the conjugacy classes of Hall subgroups of a finite permutation or matrix group. Our algorithm uses the general approach of the so-called ‘trivial Fitting model’.

MSC classification

Secondary: 20B40: Computational methods 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure 20H20: Other matrix groups over fields 20-04: Explicit machine computation and programs (not the theory of computation or programming)

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 205 - 218
Copyright
Copyright © London Mathematical Society 2012

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