Glasnik Matematicki, Vol. 45, No.2 (2010), 415-429.

COVERINGS OF FINITE GROUPS BY FEW PROPER SUBGROUPS

Yakov Berkovich

Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel

Abstract.   A connection between maximal sets of pairwise non-commuting elements and coverings of a finite group by proper subgroups is established. This allows us to study coverings of groups by few proper subgroups. The p-groups without p+2 pairwise non-commuting elements are classified. We also prove that if a p-group admits an irredundant covering by p+2 subgroups, then p=2. Some related topics are also discussed.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Minimal nonabelian p-groups, irredundant covering, minimal nonnilpotent groups, central product.

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DOI: 10.3336/gm.45.2.09

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