Subgroups of minimal index in polynomial time

Saveliy V. Skresanov

Subgroups of minimal index in polynomial time

Group Theory 2018-09-05 v2 Computational Complexity

Authors: Saveliy V. Skresanov

Abstract

Let $G$ be a finite group and let $H$ be a proper subgroup of $G$ of minimal index. By applying an old result of Y. Berkovich, we provide a polynomial algorithm for computing $|G : H|$ for a permutation group $G$ . Moreover, we find $H$ explicitly if $G$ is given by a Cayley table. As a corollary, we get an algorithm for testing whether a finite permutation group acts on a tree or not.

Keywords

finite groups minimal index subgroups polynomial time algorithm permutation groups cayley table tree action

Cite

@article{arxiv.1807.11773,
  title  = {Subgroups of minimal index in polynomial time},
  author = {Saveliy V. Skresanov},
  journal= {arXiv preprint arXiv:1807.11773},
  year   = {2018}
}

Comments

In the second version we gave the reference to Theorem 1, since it was obtained by Y. Berkovich earlier (as communcated by A. Mann), and added Theorem 3

Subgroups of minimal index in polynomial time

Abstract

Keywords

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