Modular representations and almost free actions
Modular representations and almost free actions
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模块化表示和几乎自由的动作
DOI：
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发表时间：
1995
期刊：
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通讯作者：
A. Shalev
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作者：
A. Shalev
设k是一个特征为p >0 0的域，设G是一个阶可被/?整除的有限群。利用G的非平凡元素的不动点空间都具有小维的性质，对大维的fg -模f进行了检验。证明了这种模块的存在对G.的结构有严格的限制。1991数学学科分类：20D99, 20C20。在具有小中心的自同构的研究中，人们可以关注被作用的对象，也可以关注算子群的结构。这里我们关注的是第二种类型的问题，在G是作用于线性空间K的有限群的情况下，为了精确起见，设K是一个特征为p > 0的域，设G是一个有限群。定义fcg模V的不动性fix(F) äs为非平凡元素g的不动点空间的维数上的最大值
Let k be a field of characteristic p > 0, and let G be a finite group whose order is divisible by/?. We examine fcG-modules Fof large dimension with the property that the spaces of fixed points of non-trivial elements of G all have small dimension. It is shown that the existence of such a module imposes severe restrictions on the structure of G. 1991 Mathematics Subject Classification: 20D99, 20C20. l Introduction In the study of automorphisms with small centralizers, one can focus either on the object being acted on, or on the structure of the operator group. Here we are concerned with questions of the second type, in the case where G is a finite group acting on a linear space K To make things precise, let k be a field of characteristic p > 0 and let G be a finite group. The fixity fix(F) of a fcG-module V is defined äs the maximum over the dimensions of the spaces of fixed points of non-trivial elements g e G. Thus