群中由子集定义的关系

Relations Defined by Subsets of a Group

考虑了任何群中的由一个非空子集定义的一个关系,证明了这个关系是等价关系当且仅当这个非空子集是一个子群.还研究了这个关系是偏序关系的充要条件.

Relations defined by nonempty subsets of an arbitrary group are studied. It is proved that the defined relation is an equivalence relation if and only if the nonempty subset is a subgroup. Sufficient and necessary conditions such that the defined relation is a partial ordering relation are considered.