The normal covering number $gamma(G)$ of a finite, non-cyclic group $G$ is the minimum number of proper subgroups such that each element of $G$ lies in some conjugate of one of these subgroups. We find lower bounds linear in $n$ for $gamma(S_n)$, when $n$ is even, and for $gamma(A_n)$, when $n$ is odd.
Linear bounds for the normal covering number of the symmetric and alternating groups / Bubboloni D.; Praeger C.E.; Spiga P.. - In: MONATSHEFTE FÜR MATHEMATIK. - ISSN 0026-9255. - STAMPA. - 191:(2020), pp. 229-247. [10.1007/s00605-019-01287-5]
Linear bounds for the normal covering number of the symmetric and alternating groups
Bubboloni D.
;
2020
Abstract
The normal covering number $gamma(G)$ of a finite, non-cyclic group $G$ is the minimum number of proper subgroups such that each element of $G$ lies in some conjugate of one of these subgroups. We find lower bounds linear in $n$ for $gamma(S_n)$, when $n$ is even, and for $gamma(A_n)$, when $n$ is odd.File in questo prodotto:
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