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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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
Mathematics Subject Classification (2000)
- Schur multiplier
- Lie rings
- Lazard correspondence