کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6426103 | 1345426 | 2011 | 11 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Average dimension of fixed point spaces with applications Average dimension of fixed point spaces with applications](/preview/png/6426103.png)
Let G be a finite group, F a field, and V a finite dimensional FG-module such that G has no trivial composition factor on V. Then the arithmetic average dimension of the fixed point spaces of elements of G on V is at most (1/p)dimV where p is the smallest prime divisor of the order of G. This answers and generalizes a 1966 conjecture of Neumann which also appeared in a paper of Neumann and Vaughan-Lee and also as a problem in The Kourovka Notebook posted by Vaughan-Lee. Our result also generalizes a recent theorem of Isaacs, Keller, Meierfrankenfeld, and Moretó. We also classify precisely when equality can occur. Various applications are given. For example, another conjecture of Neumann and Vaughan-Lee is proven and some results of Segal and Shalev are improved and/or generalized concerning BFC groups.
Journal: Advances in Mathematics - Volume 226, Issue 1, 15 January 2011, Pages 298-308