有限生成剩余有限群的素数阶自同构
Finitely Generated Residually Finite Groups with Automorphisms of Prime Order
DOI: 10.12677/PM.2018.85076, PDF,    国家自然科学基金支持
作者: 王志海*, 徐 涛：河北工程大学数理学院，河北 邯郸
关键词: 有限生成；剩余有限群；无不动点自同构；Finitely Generated； Residually Finite Group； Fixed-Point-Free Automorphism
摘要: 设 是有限生成剩余有限群G的素数p阶自同构，映射 是满射，则G是幂零类至多为h(p)的幂零群，其中h(p)是与素数p有关的函数。特别地，如果 是2阶自同构，那么G是交换群。
Abstract: Let be an automorphism of prime order p of a finitely generated residually finite group G. If the map defined by is surjective, then G is nilpotent of class at most h(p), where h(p) is a function depending only on p. In particular, if is of order 2, then G is abelian.
文章引用：王志海, 徐涛. 有限生成剩余有限群的素数阶自同构[J]. 理论数学, 2018, 8(5): 576-579. https://doi.org/10.12677/PM.2018.85076

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