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Computing Hall subgroups of finite groups. (English) Zbl 1296.20017

Summary: 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:

20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20E45 Conjugacy classes for groups
20B35 Subgroups of symmetric groups
20G40 Linear algebraic groups over finite fields
20-04 Software, source code, etc. for problems pertaining to group theory
68W30 Symbolic computation and algebraic computation

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