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

摘要

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.