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Schur multipliers and the Lazard correspondence

机译:舒尔乘数与拉扎德对应

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摘要

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.
机译:令G为小于p-1的幂等性类的有限p组,令L为通过Lazard对应于G的Lie环。我们表明G和L的Schur乘数是同构的阿贝尔群,并且G的每个Schur覆盖都与L的Schur封面在Lazard对应。此外,我们证明G和L的震中是同构的阿贝尔群。因此,当且仅当Lie环L具有能力时,基团G才具有能力。

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