Abstract

We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determinant work by Edward Formanek, David Sibley, and Richard Mansfield, where they show that two groups with the same group determinant are isomorphic. The derived condition leads to a generalization of this result.

中文翻译：

---

广义群行列式为有限群的子集成为子群提供了充要条件

摘要

我们概括了群决定因素的概念，并证明了一个子集成为子群的必要和充分的新颖条件。此发展基于Edward Formanek，David Sibley和Richard Mansfield的组决定因素工作，他们表明具有相同组决定因素的两个组是同构的。导出的条件导致该结果的一般化。