HallSubgroup( G, n )
HallSubgroup( G, L )
Let G be an ag group. Then
HallSubgroup returns a
pi-Hall-subgroup of G for the set pi of all prime divisors of the
integer n or the join pi of all prime divisors of the integers of
The Hall-subgroup is constructed using Glasby's algorithm (see
Gla87), which descends along an elementary abelian series for G
and constructs complements in the coprime case (see CoprimeComplement).
If no such series is known for G the function uses
ElementaryAbelianSeries (see ElementaryAbelianSeries) in order to
construct such a series for G.
gap> HallSubgroup( s4, 2 ); Subgroup( s4, [ a, c, d ] ) gap> HallSubgroup( s4, [ 3 ] ); Subgroup( s4, [ b ] ) gap> z5 := CyclicGroup( AgWords, 5 ); Group( c5 ) gap> DirectProduct( s4, z5 ); Group( a1, a2, a3, a4, b ) gap> HallSubgroup( last, [ 5, 3 ] ); Subgroup( Group( a1, a2, a3, a4, b ), [ a2, b ] )
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