A Note on Maximal Coverings of Groups

Abstract

Let λ(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 λ(G), classify the groups for which λ(G) = 3, 4, 5 and also classify the nilpotent groups that admit only one-sized coverings.

Key Words:

• Irredundant covering
• Maximal
• Subgroup

2010 Mathematics Subject Classification:

• Primary 20E07, 20E28
• Secondary 20D60, 20D15

ACKNOWLEDGMENTS

The author would like to thank Emanuel Carneiro for fruitful conversations during the preparation of this work.

Notes

Communicated by J. Zhang.