Schur multipliers and the Lazard correspondence
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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
KeywordsSchur multiplier p-groups Lie rings Lazard correspondence
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