On covers of abelian groups by cosets
| dc.creator | Lettl, Günter | |
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2004-11-07 | |
| dc.date | 2008-03-11 | |
| dc.date.accessioned | 2026-07-07T09:25:59Z | |
| dc.date.available | 2026-07-07T09:25:59Z | |
| dc.description | Let G be any abelian group and {a_sG_s}_{s=1}^k be a finite system of cosets of subgroups G_1,...,G_k. We show that if {a_sG_s}_{s=1}^k covers all the elements of G at least m times with the coset a_tG_t irredundant then [G:G_t]\le 2^{k-m} and furthermore k\ge m+f([G:G_t]), where f(\prod_{i=1}^r p_i^{alpha_i})=\sum_{i=1}^r alpha_i(p_i-1) if p_1,...,p_r are distinct primes and alpha_1,...,alpha_r are nonnegative integers. This extends Mycielski's conjecture in a new way and implies a conjecture of Gao and Geroldinger. Our new method involves algebraic number theory and characters of abelian groups. | |
| dc.description | 10 pages, also related to Number Theory and Combinatorics | |
| dc.identifier | https://arxiv.org/abs/math/0411144 | |
| dc.identifier | http://arxiv.org/abs/math/0411144 | |
| dc.identifier | Acta Arith. 131(2008), no.4, 341-350 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156598 | |
| dc.subject | Group Theory | |
| dc.subject | Number Theory | |
| dc.subject | 20K99; 05D99, 05E99; 11B25; 11B75; 11R04; 11S99; 20C15; 20D60 | |
| dc.title | On covers of abelian groups by cosets | |
| dc.type | text |