Profinite groups and the fixed points of coprime automorphisms

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• 作者：Cristina Acciarri ; ^{acciarricristina@yahoo.it" class="auth_mail" title="E-mail the corresponding author} ; Pavel Shumyatsky ^{pavel@unb.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：20E18 ; 20E25 ; 20F40
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：452
• 期：Complete
• 页码：188-195
• 全文大小：280 K

文摘

The main result of the paper is the following theorem. Let q be a prime and A   an elementary abelian group of order q³$q^3$. Suppose that A acts coprimely on a profinite group G   and assume that C_G(a)$C_G(a)$ is locally nilpotent for each a∈A^#$a\in A^{\mathrm{\#}}$. Then the group G is locally nilpotent.