English

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

R2 v1 2026-06-21T11:00:22.010Z