| | |
| | |
Stat |
Members: 3645 Articles: 2'501'711 Articles rated: 2609
20 April 2024 |
|
| | | |
|
Article forum
| |
|
On the Herzog-Schönheim conjecture for uniform covers of groups | Zhi-Wei Sun
; | Date: |
5 Jun 2003 | Journal: | J. Algebra 273(2004), no. 1, 153--175 | Subject: | Group Theory; Number Theory MSC-class: 20D60; 05A18; 11B25; 11N45; 20D20; 20D35; 20E15; 20F16 | math.GR math.NT | Abstract: | Let G be any group and $a_1G_1,...,a_kG_k (k>1)$ be left cosets in G. In 1974 Herzog and Schönheim conjectured that if $Cal A={a_iG_i}_{i=1}^k$ is a partition of G then the (finite) indices $n_1=[G:G_1],...,n_k=[G:G_k]$ cannot be distinct. In this paper we show that if $Cal A$ covers all the elements of G the same times and $G_1,...,G_k$ are subnormal subgroups of G not all equal to G, then $M=max_{1le jle k}|{1le ile k:n_i=n_j}|$ is not less than the smallest prime divisor of $n_1... n_k$, moreover $min_{1ls ils k}log n_i=O(Mlog^2 M)$ where the O-constant is absolute. | Source: | arXiv, math.GR/0306099 | Other source: | [GID 140358] math.GR/0306099 | Services: | Forum | Review | PDF | Favorites |
|
|
No message found in this article forum.
You have a question or message about this article?
Ask the community and write a message in the forum.
If you want to rate this article, please use the review section..
To add a message in the forum, you need to login or register first. (free): registration page
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |