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Conjectures on the normal covering number of finite symmetric and alternating groupsBubboloni, Daniela ; Praeger, Cheryl E. ; Spiga, PabloLet ▫$\gamma(S_n)$▫ 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.Source: International journal of group theory. - ISSN 2251-7650 (Vol. 3, no. 2, June 2014, str. 57-75)Type of material - article, component part ; adult, seriousPublish date - 2014Language - englishCOBISS.SI-ID - 18713433
Author
Bubboloni, Daniela |
Praeger, Cheryl E. |
Spiga, Pablo
Topics
covering |
symmetric group |
alternating group |
Magma
source: International journal of group theory. - ISSN 2251-7650 (Vol. 3, no. 2, June 2014, str. 57-75)
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Bubboloni, Daniela | |
Praeger, Cheryl E. | 12181 |
Spiga, Pablo |
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