Finite covers of groups by cosets or subgroups
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2005-01-25 | |
| dc.date | 2006-11-09 | |
| dc.date.accessioned | 2026-07-07T06:39:21Z | |
| dc.date.available | 2026-07-07T06:39:21Z | |
| dc.description | This paper deals with combinatorial aspects of finite covers of groups by cosets or subgroups. Let $a_1G_1,...,a_kG_k$ be left cosets in a group $G$ such that ${a_iG_i}_{i=1}^k$ covers each element of $G$ at least $m$ times but none of its proper subsystems does. We show that if $G$ is cyclic, or $G$ is finite and $G_1,...,G_k$ are normal Hall subgroups of $G$, then $k\geq m+f([G:\bigcap_{i=1}^kG_i])$, where $f(\prod_{t=1}^r p_t^{α_t})=\sum_{t=1}^rα_t(p_t-1)$ if $p_1,...,p_r$ are distinct primes and $α_1,...,α_r$ are nonnegative integers. When all the $a_i$ are the identity element of $G$ and all the $G_i$ are subnormal in $G$, we prove that there is a composition series from $\bigcap_{i=1}^kG_i$ to $G$ whose factors are of prime orders. The paper also includes some other results and two challenging conjectures. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0501451 | |
| dc.identifier | http://arxiv.org/abs/math/0501451 | |
| dc.identifier | Internat. J. Math. 17(2006), 1047--1064 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101043 | |
| dc.subject | Group Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20D60; 05A05; 11B25 | |
| dc.title | Finite covers of groups by cosets or subgroups | |
| dc.type | text |