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A note on maximal coverings of groups. (English) Zbl 1304.20043

Summary: Let \(\lambda(G)\) be the maximum number of subgroups in an irredundant covering of the finite group \(G\). In this note we investigate the basic properties of \(\lambda(G)\), classify the groups for which \(\lambda(G)=3\), \(4\), \(5\) and also classify the nilpotent groups that admit only one-sized coverings.

MSC:

20D60 Arithmetic and combinatorial problems involving abstract finite groups
20D30 Series and lattices of subgroups
20D15 Finite nilpotent groups, \(p\)-groups
20E28 Maximal subgroups
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