Bertrand公设与子群增长
Bertrand's postulate and subgroup growth
摘要：
在这篇文章中，我们研究了群上某些函数的L^1-范数，称为整除函数。利用这些功能，他们的连接到剩余有限性，并在投射有限群的积分理论，我们定义了剩余平均的有限生成群。本文的主要结果之一是关于有限生成线性群上剩余平均的有限性。剩余平均是否有限取决于有限指数子群的指数增长率。我们的指数增长率的结果是类似的素数之间的差距的结果，并提供了一个变体的子群增长函数，这可能是独立的利益。
英文摘要：
In this article we investigate the L^1-norm of certain functions on groups called divisibility functions. Using these functions, their connection to residual finiteness, and integration theory on profinite groups, we define the residual average of a finitely generated group. One of the main results in this article is the finiteness of residual averages on finitely generated linear groups. Whether or not the residual average is finite depends on growth rates of indices of finite index subgroups. Our results on index growth rates are analogous to results on gaps between primes, and provide a variant of the subgroup growth function, which may be of independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
