On subgroups of minimal index

07/31/2018

∙

by   Saveliy V. Skresanov, et al.

∙

0

∙

share

Let G be a group possessing a proper subgroup of finite index. We prove that if H is a proper subgroup of G of minimal index, then G/core_G(H) is a (finite) simple group. As a corollary, a polynomial algorithm for computing |G : H| for a finite permutation group G is suggested. The latter result yields an algorithm for testing whether a finite permutation group acts on a tree or not.