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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 G. It is the core of a Sylow p-subgroup of G. The p-core is often denoted Op(G), and in particular appears in the definition of the Fitting subgroup of a finite group.
Last updated: 05-21-2005 18:57:22
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details