| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
28 March 2024 |
|
| | | |
|
Article overview
| |
|
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 review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |