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).
GAP 3.4.4