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

Daniela Bubboloni; Cheryl E. Praeger; Pablo Spiga

doi:10.1007/s00605-019-01287-5

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

Daniela Bubboloni, Cheryl E. Praeger, Pablo Spiga

Mathematics and Statistics

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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 language	English
Pages (from-to)	229-247
Number of pages	19
Journal	Monatshefte fur Mathematik
Volume	191
Issue number	2
Early online date	20 Mar 2019
DOIs	https://doi.org/10.1007/s00605-019-01287-5
Publication status	Published - 1 Feb 2020

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10.1007/s00605-019-01287-5

Bubboloni et al 2019 Linear bounds for the normal covering
This is a post-peer-review, pre-copyedit version of an article published in Monatshefte für Mathematik. The final authenticated version is available online at: https://doi.org/10.1007/s00605-019-01287-5
Accepted author manuscript, 347 KB

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

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Permutation Groups & their Interrelationship with the Symmetry of Graphs Codes & Geometric Configurations

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

Abstract

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Permutation Groups & their Interrelationship with the Symmetry of Graphs Codes & Geometric Configurations

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