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Mathematics > Group Theory

arXiv:1807.11773 (math)
[Submitted on 31 Jul 2018 (v1), last revised 1 Sep 2018 (this version, v2)]

Title:Subgroups of minimal index in polynomial time

Authors:Saveliy V. Skresanov
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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.
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
Subjects: Group Theory (math.GR); Computational Complexity (cs.CC)
MSC classes: 20E28, 20B40, 05E18
Cite as: arXiv:1807.11773 [math.GR]
  (or arXiv:1807.11773v2 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.1807.11773

Submission history

From: Saveliy Skresanov [view email]
[v1] Tue, 31 Jul 2018 11:55:40 UTC (5 KB)
[v2] Sat, 1 Sep 2018 11:17:11 UTC (4 KB)
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