Normal coverings of finite symmetric and alternating groups
Group Theory
2010-11-22 v1
Abstract
In this paper we investigate the minimum number of maximal subgroups H_i for i=1 ...k of the symmetric group S_n (or the alternating group A_n) such that each element in the group S_n (respectively A_n) lies in some conjugate of one of the H_i. We prove that this number lies between a.phi(n) and bn for certain constants a, b, where phi(n) is the Euler phi-function, and we show that the number depends on the arithmetical complexity of n. Moreover in the case where n is divisible by at most two primes, we obtain an upper bound of 2+phi(n)/2, and we determine the exact value for S_n when n is odd and for A_n when n is even.
Keywords
Cite
@article{arxiv.1011.4368,
title = {Normal coverings of finite symmetric and alternating groups},
author = {Daniela Bubboloni and Cheryl Praeger},
journal= {arXiv preprint arXiv:1011.4368},
year = {2010}
}