Irredundant and Minimal Covers of Finite Groups

Abstract

A cover of a finite noncyclic group G is a family ℋ of proper subgroups of G whose union equals G. A cover of G is called minimal if it has minimal size, and irredundant if it does not properly contain any other cover. We classify the finite noncyclic groups all of whose irredundant covers are minimal.

Key Words:

• Minimal covers
• Irredundant covers
• Maximal cyclic subgroups

2010 Mathematics Subject Classification:

• 20B05