有限幂零群通过对称群扩张的整群环的正规化子性质  

The Normalizer Property for Integral Group Rings of Extensions of Finite Nilpotent Groups by Symmetric Groups

作　　者：李正兴[1] 海进科[1] 

机构地区：[1]青岛大学数学科学学院,青岛266071

出　　处：《数学学报（中文版）》2013年第4期519-526,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11171169;11071155);山东省优秀中青年科学家科研奖励基金(BS2012SF003)

摘　　要：设G是一个有限幂零群Ⅳ通过m次对称群S_m的扩张,本文证明了G有正规化子性质.我们的定理推广了Petit Lobao与Sehgal的一个结果:设G=N(?) S_m是一个有限幂零群N与对称群S_m的自然圈积,则G有正规化子性质.我们的方法不同于Petit Lobao与Sehgal的方法.Let G be an extension of a finite nilpotent group N by a symmetric group Sm of degree m. It is shown that, the normalizer property holds for G. This generalizes a result due to Petit Lobao and Sehgal which states that, if G = N Sm is the natural wreath product of a finite nilpotent group N by a symmetric group Sm of degree m, then the normalizer property holds for G. Techniques used in this paper are different from that used by Petit Lobao and Sehgal.

关 键 词：整群环 对称群 正规化子性质 

分 类 号：O152.6[理学—数学]