Linear bounds for the normal covering number of the symmetric and alternating groups

Daniela Bubboloni, Cheryl E. Praeger, Pablo Spiga

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Abstract

The normal covering number γ(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 γ(S n ) , when n is even, and for γ(A n ) , when n is odd.

Original languageEnglish
Number of pages19
JournalMonatshefte fur Mathematik
DOIs
Publication statusE-pub ahead of print - 20 Mar 2019

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