### Finite groups that are the union of at most 25 proper subgroups.Finite groups that are the union of at most 25 proper subgroups.

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 Author Garonzi, Martino Source CiteSeerX Content type Text File Format PDF
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Proper Subgroup ♦ Finite Group ♦ Set-theoretical Union ♦ Finite Group Let ♦ Elementary Group ♦ Non-trivial Normal Subgroup 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 article 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. 1 Educational Role Student ♦ Teacher Age Range above 22 year Educational Use Research Education Level UG and PG ♦ Career/Technical Study Learning Resource Type Article