Normal coverings of finite symmetric and alternating groups

Daniela Bubboloni; Cheryl Praeger

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arXiv · 1011.4368

Normal coverings of finite symmetric and alternating groups

Daniela Bubboloni·Cheryl Praeger

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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.

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BibTeX RIS

Daniela Bubboloni, Cheryl Praeger. 2010-11-19. Normal coverings of finite symmetric and alternating groups. https://arxiv.org/abs/1011.4368

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