On the Herzog-Schönheim conjecture for uniform covers of groups
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2003-06-05 | |
| dc.date | 2004-12-30 | |
| dc.date.accessioned | 2026-07-07T04:58:37Z | |
| dc.date.available | 2026-07-07T04:58:37Z | |
| dc.description | 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 $M=\max_{1\le j\le k}|\{1\le i\le k:n_i=n_j\}|$ is not less than the smallest prime divisor of $n_1... n_k$, moreover $\min_{1\ls i\ls k}\log n_i=O(M\log^2 M)$ where the O-constant is absolute. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0306099 | |
| dc.identifier | http://arxiv.org/abs/math/0306099 | |
| dc.identifier | J. Algebra 273(2004), no. 1, 153--175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67707 | |
| dc.subject | Group Theory | |
| dc.subject | Number Theory | |
| dc.subject | 20D60; 05A18; 11B25; 11N45; 20D20; 20D35; 20E15; 20F16 | |
| dc.title | On the Herzog-Schönheim conjecture for uniform covers of groups | |
| dc.type | text |