On Sun's conjecture concerning disjoint cosets
Group Theory
2008-07-15 v1 Number Theory
Abstract
In 2004, Zhi-Wei Sun posed the following conjecture: If a_1G_1,...,a_kG_k (k>1) are finitely many pairwise disjoint left cosets in a group G with all the indices [G:G_i] finite, then for some 1\le i<j\le k, the greatest common divisor of [G:G_i] and [G:G_j] is at least k. In this paper, we confirm Sun's conjecture for k=3,4.
Cite
@article{arxiv.0807.2207,
title = {On Sun's conjecture concerning disjoint cosets},
author = {Wan-Jie Zhu},
journal= {arXiv preprint arXiv:0807.2207},
year = {2008}
}
Comments
10 pages