We study the problem of finding a subgroup of a given order in a finite group, where the group is represented by its Cayley table. We analyze the complexity of the problem in the special case of abelian groups and present an optimal algorithm for finding a subgroup of a given order when the input is given in the form of a Cayley table. To the best of our knowledge, no prior work has addressed the complexity of this problem under the Cayley table representation.

翻译：本文研究在有限群中寻找给定阶子群的问题，其中群由其凯莱表表示。我们分析了该问题在阿贝尔群特殊情况下的复杂性，并提出了一种在输入以凯莱表形式给出时寻找给定阶子群的最优算法。据我们所知，此前尚未有研究探讨凯莱表表示下该问题的复杂性。