Extraspecial commutator-in-center subgroup is central factor

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Revision as of 21:45, 7 July 2008 by Vipul (talk | contribs) (New page: ==Statement== ===Statement with symbols=== Let <math>G</math> be a finite <math>p</math>-group, i.e. a group of prime power order. Suppose <math>H</math> is a subgroup of <math>G</mat...)
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Statement

Statement with symbols

Let G be a finite p-group, i.e. a group of prime power order. Suppose H is a subgroup of G satisfying the following two conditions:

  1. H is an extraspecial group
  2. [G,H] \le Z(H)

Then HC_G(H) = G, i.e., H is a central factor of G.