ALL libraries (COBIB.SI union bibliographic/catalogue database)
13.
Conjectures on the normal covering number of finite symmetric and alternating groups
Bubboloni, Daniela ; Praeger, Cheryl E. ; Spiga, Pablo
Let ▫$\gamma(S_n)$▫ be the minimum number of proper subgroups ▫$H_i$, $i=1, \ldots, l$▫ of the symmetric group ▫$S_n$▫ such that each element in ▫$S_n$▫ lies in some conjugate of one of the ▫$H_i$▫. ...In this paper we conjecture that ▫$$ \gamma(S_n)=\frac{n}{2}\bigg(1-\frac{1}{p_1}\bigg) \bigg(1-\frac{1}{p_2}\bigg)+2, $$▫ where ▫$p_1,p_2$▫ are the two smallest primes in the factorization of ▫$n\in\mathbb{N}$▫ and ▫$n$▫ is neither a prime power nor a product of two primes. Support for the conjecture is given by a previous result for ▫$n=p_1^{\alpha_{1}}p_2^{\alpha_{2}},$▫ with ▫$(\alpha_1,\alpha_2)\neq (1,1)$▫. We give further evidence by confirming the conjecture for integers of the form ▫$n=15q$▫ for an infinite set of primes ▫$q$▫, and by reporting on a Magma computation. We make a similar conjecture for ▫$\gamma(A_n)$▫, when ▫$n$▫ is even and provide a similar amount of evidence.
It was not necessary to add the material to the shelf.
Bibliographic material was successfully added on shelf.
Adding bibliographical material on shelf was not successful.
Material is already on the shelf.
Permalink
URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year
Impact factor
Edition
Category
Classification
JCR
SNIP
JCR
SNIP
JCR
SNIP
JCR
SNIP
Select the library membership card:
DRS,
in which the journal is indexed
Database name
Field
Year
Links to authors' personal bibliographies
Links to information on researchers in the SICRIS system
Subject headings in COBISS General List of Subject Headings
Select pickup location
The material from the parent unit is free. If the material is delivered to the pickup location from another unit, the library may charge you for this service.
