๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Packing and Covering Groups with Subgroups

โœ Scribed by D. Jungnickel; L. Storme

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
182 KB
Volume
239
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

โœฆ Synopsis

We study the problem of covering or packing a finite group with subgroups of a specified order and obtain bounds on the size of such covers and packings. Our main results provide characterizations of the elementary abelian groups by the existence of large packings or small covers, respectively. Hence large packings and small covers can be thought of as geometric objects: they correspond to large ลฝ . partial t-spreads and small t-covers of a suitable projective space PG d, p for some prime p. We shall also exhibit some series of examples which show that our bounds are reasonable.

๐Ÿ“œ SIMILAR VOLUMES

Packing and covering dense graphs
Packing and covering dense graphs
โœ Noga Alon; Yair Caro; Raphael Yuster ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 498 KB ๐Ÿ‘ 1 views
Groups with Many FC-Subgroups
Groups with Many FC-Subgroups
โœ Silvana Franciosi; Francesco de Giovanni; Yaroslav P. Sysak ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 120 KB

DEDICATED TO DEREK J. S. ROBINSON ON THE OCCASION OF HIS 60TH BIRTHDAY ## 1. Introduction A group G is called an FC-group if every element x of G has only ลฝ . finitely many conjugates in G, that is, if the centralizer C x has finite G index in G. There exists a wide literature on this subject, and

Covering and Packing Problems in Lattice
Covering and Packing Problems in Lattices Associated with then-Cube
โœ Horst Martini; Walter Wenzel ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 145 KB

We study optimal coverings of lattices associated with a given n-cube by frames (= Hamming spheres of radius one) and extended frames under certain constraints, e.g., by constituting at the same time packings of the edge system in such finite lattices. These investigations also yield results on diff

Kirkman packing and covering designs wit
Kirkman packing and covering designs with spanned holes of size 2
โœ Jianxing Yin ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 120 KB ๐Ÿ‘ 1 views

## Abstract A Kirkman holey packing (resp. covering) design, denoted by KHPD(__g^u^__) (resp. KHCD(__g^u^__)), is a resolvable (__gu__, 3, 1) packing (resp. covering) design of pairs with __u__ disjoint holes of size __g__, which has the maximum (resp. minimum) possible number of parallel classes.