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

(Submitted)

Author: Erg\" un Yal\c c\i n

2000 Mathematics Subject Classification.
Primary: 20J06; Secondary: 20D15, 20D60, 51E20.

Address: 
Department of Mathematics
Bilkent University
Ankara, Turkey 

Abstract:
We define a group theoretical invariant, denoted by $s(G)$,
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 $s(G)$, we 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.