Schur multipliers and the Lazard correspondence

被引：16

作者：

Eick, Bettina ^{[1
]}

Horn, Max ^{[1
]}

Zandi, Seiran ^{[2
]}

机构：

[1] Tech Univ Carolo Wilhelmina Braunschweig, D-38106 Braunschweig, Germany

[2] Tarbiat Moallem Univ, Dept Math Sci, Tehran, Iran

来源：

ARCHIV DER MATHEMATIK | 2012年 / 99卷 / 03期

关键词：

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

D O I：

10.1007/s00013-012-0426-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：217 / 226

页数：10

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