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Archiv der Mathematik

, Volume 99, Issue 3, pp 217–226 | Cite as

Schur multipliers and the Lazard correspondence

  • Bettina Eick
  • Max Horn
  • Seiran Zandi
Article

Abstract

Let G be a finite p-group of nilpotency class less than p−1, and let L be the Lie ring corresponding to G via the Lazard correspondence. We show that the Schur multipliers of G and L are isomorphic as abelian groups and that every Schur cover of G is in Lazard correspondence with a Schur cover of L. Further, we show that the epicenters of G and L are isomorphic as abelian groups. Thus the group G is capable if and only if the Lie ring L is capable.

Mathematics Subject Classification (2000)

17B30 20D15 20F18 20F40 

Keywords

Schur multiplier p-groups Lie rings Lazard correspondence 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.TU BraunschweigBraunschweigGermany
  2. 2.Department of Mathematical SciencesTarbiat Moallem UniversityTehranIran

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