论文标题
通过减少当地问题来确定非亚伯群体和模块的措施
Identifying measures on non-abelian groups and modules by their moments via reduction to a local problem
论文作者
论文摘要
关于Cohen-Lenstra和Cohen-Martinet启发式方法的概括，它引起了人们对涂鸦类同构类别的概率度量的关注。正如概率理论中的常见一样，需要知道这些措施取决于它们的力矩决定，在这种情况下，这是固定有限群体的预期冲销数量。我们展示了一系列的措施，包括在最近的刘，伍德和祖里克·布朗的一篇论文中出现的措施，具有这种属性。该方法是通过有限简单组的产物“本地”与固定组扩展的组一起工作。这最终将问题降低到固定有限简单组的权力情况下，可以通过简单的显式计算来处理。我们还可以证明对代数上的随机模块是类似的定理。
Work on generalizations of the Cohen-Lenstra and Cohen-Martinet heuristics has drawn attention to probability measures on the space of isomorphism classes of profinite groups. As is common in probability theory, it would be desirable to know that these measures are determined by their moments, which in this context are the expected number of surjections to a fixed finite group. We show a wide class of measures, including those appearing in a recent paper of Liu, Wood, and Zurieck-Brown, have this property. The method is to work "locally" with groups that are extensions of a fixed group by a product of finite simple groups. This eventually reduces the problem to the case of powers of a fixed finite simple group, which can be handled by a simple explicit calculation. We can also prove a similar theorem for random modules over an algebra.
