Finite Groups that are the union of at most 25 proper subgroups

2011/12/26 by Martino Garonzi, Garonzi, Martino · 2 citations
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1112.5892

arxiv created 2011/12/26 · arxiv updated 2011/12/30

Abstract

For a finite group G let σ(G) (the "sum" of G) be the least number of proper subgroups of G whose set-theoretical union is equal to G, and σ(G)=∞ if G is cyclic. We say that a group G is σ-elementary if for every non-trivial normal subgroup N of G we have σ(G)<σ(G/N). In this paper we produce the list of all the σ-elementary groups of sum up to 25. We also show that σ(\Aut(PSL(2,8)))=29.

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