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Schur multipliers and the Lazard correspondence

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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.

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Correspondence to Bettina Eick.

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Eick, B., Horn, M. & Zandi, S. Schur multipliers and the Lazard correspondence. Arch. Math. 99, 217–226 (2012). https://doi.org/10.1007/s00013-012-0426-7

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Mathematics Subject Classification (2000)

  • 17B30
  • 20D15
  • 20F18
  • 20F40

Keywords

  • Schur multiplier
  • p-groups
  • Lie rings
  • Lazard correspondence