On the covering number of symmetric groups of even degree

2014/10/28 by Eric Swartz, Swartz, Eric
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1410.7524

Manuscript has been completely rewritten to fix gaps in proofs and improve readability

arxiv created 2016/02/03 · arxiv updated 2016/02/04

Abstract

If a group G is the union of proper subgroups H₁, …, H_k, we say that the collection \H₁, … H_k \ is a cover of G, and the size of a minimal cover (supposing one exists) is the covering number of G, denoted σ(G). Maróti showed that σ(S_n) = 2^n-1 for n odd and sufficiently large, and he also gave asymptotic bounds for n even. In this paper, we determine the exact value of σ(S_n) when n is divisible by 6.

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