GAP Manual: 7.28. PCore

PCore( G, p )

PCore returns the p-core of the finite group G for a prime p.

The p-core is the largest normal subgroup whose size is a power of p. This is the core of the Sylow-p-subgroups (see Core and SylowSubgroup).

Note that PCore sets and tests G.pCores[ p ].

    gap> s4 := Group( (1,2,3,4), (1,2) );
    Group( (1,2,3,4), (1,2) )
    gap> PCore( s4, 2 );
    Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,4)(2,3), (1,3)(2,4) ] )
    gap> PCore( s4, 3 );
    Subgroup( Group( (1,2,3,4), (1,2) ), [  ] ) 

The default function GroupOps.PCore computes the p-core as the core of a Sylow-p-subgroup (see Core and SylowSubgroup).