A cancellation theorem for modules over integral group rings
A cancellation theorem for modules over integral group rings
复制标题
DOI：
10.1017/s0305004120000237
复制
发表时间：
2018-07
影响因子：
0.8
通讯作者：
John Nicholson
中科院分区：
文献类型：
--
作者：
John Nicholson
一个长期存在的问题，其根源在低维同伦理论，是分类所有的有限群G，其整群环G的稳定自由消除（SFC）。推广了R. G. Swan给出了SFC的一个条件，并利用这个条件证明了如果至多有一个四元数的拷贝出现在真实的群环的Wedderburn分解中，则群环具有SFC.这推广了整群环情况下的艾希勒条件。
A long standing problem, which has its roots in low-dimensional homotopy theory, is to classify all finite groups G for which the integral group ring ℤG has stably free cancellation (SFC). We extend results of R. G. Swan by giving a condition for SFC and use this to show that ℤG has SFC provided at most one copy of the quaternions ℍ occurs in the Wedderburn decomposition of the real group ring ℝG. This generalises the Eichler condition in the case of integral group rings.