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Set Covering and Serre's Theorem on the Cohomology Algebra of a p-Group

We define a group theoretical invariant, denoted by sG� , as a solution of a certain set covering problem and show that it is closely related to chl(G), the cohomology length of a p-group G. By studying sGwe improve the known upper bounds for the cohomology length of a p-group and determine chl(G) completely for extra-special 2-groups of real type.  2001 Academic Press