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›› 2013, Vol. 30 ›› Issue (3): 289-292.DOI: 10.7523/j.issn.1002-1175.2013.03.001

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A note on the kernel group of an integral group ring

LIU Jia, TANG Guo-Ping   

  1. School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing 100049, China
  • Received:2012-03-28 Revised:2012-05-15 Online:2013-05-15

Abstract:

Let G be a finite group, Λ be a Z-order of group algebra QG, and Λ' be a maximal Z-order containing Λ. There is a homomorphism between locally free groups CL(Λ) and CL(Λ') which is induced by including map, and the kernel group D(Λ) is defined to be the kernel of this homomorphism. When G is a p-group, we give an estimate of the exponent of the kernel group D(ZG).

Key words: integral group ring, kernel group D(ZG), maximal Z-order

CLC Number: