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      A note on Serre ' s theorem in group cohomology

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      Author(s)
      Yalçin, E.
      Date
      2008
      Source Title
      Proceedings of the American Mathematical Society
      Print ISSN
      0002-9939
      Electronic ISSN
      1088-6826
      Publisher
      American Mathematical Society
      Volume
      136
      Issue
      8
      Pages
      2655 - 2663
      Language
      English
      Type
      Article
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      Abstract
      In 1987, Serre proved that if G is a p-group which is not elementary abelian, then a product of Bocksteins of one dimensional classes is zero in the mod p cohomology algebra of G, provided that the product includes at least one nontrivial class from each line in H1 (G,Fp). For p = 2, this gives that (σG) = 0, where σG is the product of all nontrivial one dimensional classes in H1 (G, F 2). In this note, we prove that if G is a nonabelian 2-group, then σG is also zero. © 2008 American Mathematical Society.
      Keywords
      Cohomology of groups
      Essential cohomology
      Stiefel - Whitney classes
      Permalink
      http://hdl.handle.net/11693/23050
      Published Version (Please cite this version)
      http://dx.doi.org/10.1090/S0002-9939-08-09408-2
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