Page 67 - Ellingham, Mark, Mariusz Meszka, Primož Moravec, Enes Pasalic, 2014. 2014 PhD Summer School in Discrete Mathematics. Koper: University of Primorska Press. Famnit Lectures, 3.
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Some Topics in the Theory of Finite
Groups
Primož Moravec
University of Ljubljana, Slovenia
SUMMARY
The theory of finite groups plays a central role in group theory and has several applica-
tions in other branches of mathematics, including discrete mathematics and cryptogra-
phy. The theory culminated with the classification of finite simple groups in 1983, and
has developed afterwards into several different directions such as the theory of groups
of prime power order, invariant theory, and many others. This mini course will address
some topics of the above theory. These will include advanced applications of Sylow’s
theory, techniques of building new groups from old, basic theory of finite p-groups, and
problems regarding enumeration of finite groups.
55
Some Topics in the Theory of Finite
Groups
Primož Moravec
University of Ljubljana, Slovenia
SUMMARY
The theory of finite groups plays a central role in group theory and has several applica-
tions in other branches of mathematics, including discrete mathematics and cryptogra-
phy. The theory culminated with the classification of finite simple groups in 1983, and
has developed afterwards into several different directions such as the theory of groups
of prime power order, invariant theory, and many others. This mini course will address
some topics of the above theory. These will include advanced applications of Sylow’s
theory, techniques of building new groups from old, basic theory of finite p-groups, and
problems regarding enumeration of finite groups.
55
