Let γ(Sn) be the minimum number of proper subgroups Hi, i = 1,..., l of the symmetric group Sn such that each element in Sn lies in some conjugate of one of the Hi. In this paper we conjecture that where p1; p2 are the two smallest primes in the factorization of n ∈ 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 = p1 α1 p2 α2, with (α1, α2) ≠ (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 γ(An), when n is even, and provide a similar amount of evidence. © 2013 University of Isfahan.
Bubboloni, D., Praeger, C., & Spiga, P. (2014). Conjectures on the normal covering number of the finite symmetric and alternating groups. INTERNATIONAL JOURNAL OF GROUP THEORY, 3(2), 57-75.
Citazione: | Bubboloni, D., Praeger, C., & Spiga, P. (2014). Conjectures on the normal covering number of the finite symmetric and alternating groups. INTERNATIONAL JOURNAL OF GROUP THEORY, 3(2), 57-75. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Presenza di un coautore afferente ad Istituzioni straniere: | Si |
Titolo: | Conjectures on the normal covering number of the finite symmetric and alternating groups |
Autori: | Bubboloni, D; Praeger, C; Spiga, P |
Autori: | SPIGA, PABLO (Ultimo) |
Data di pubblicazione: | 2014 |
Lingua: | English |
Rivista: | INTERNATIONAL JOURNAL OF GROUP THEORY |
Appare nelle tipologie: | 01 - Articolo su rivista |
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