Core (group)

In mathematics, the core of a subgroup H of a group G with respect to a subset S of elements of G is defined to be the intersection of the subgroups conjugate to H under every element of the set S. In the special case when S = G it follows that the core of H is the largest normal subgroup of G contained in H.

For a prime p, the p-core is defined to be the largest normal p-group in <math>G<math>. It is the core of a Sylow p-subgroup of <math>G<math>. The p-core is often denoted <math>O_p(G)<math>, and in particular appears in the definition of the Fitting subgroup of a finite group.