关于群体增长的缺口猜想
On the Gap Conjecture concerning group growth
摘要：
我们讨论了关于群增长的Gap猜想的一些新结果，并给出了它（及其 *-版本）到几类特殊群的一个约化。也就是说，我们证明了它对单群类和剩余有限群类的有效性将完全普遍地蕴涵Gap猜想。如果该猜想对剩余多环群且仅对-无限群有效，则类似类型的归约成立。还考虑了剩余可解群和右可序群的情形。
英文摘要：
We discuss some new results concerning Gap Conjecture on group growth and present a reduction of it (and its *-version) to several special classes of groups. Namely we show that its validity for the classes of simple groups and residually finite groups will imply the Gap Conjecture in full generality. A similar type reduction holds if the Conjecture is valid for residually polycyclic groups and just-infinite groups. The cases of residually solvable groups and right orderable groups are considered as well.
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