Computational Complexity of Finding Subgroups of a Given Order

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.