Publication year: 2007
: 978-88-470-0623-2
Born from the university courses of Group Theory held by the author for several years, this book deals with the fundamental arguments of the theory: abelian, nilpotent and solvable groups, free groups, permutations, representations and cohomology. After the first notions, Hölder's program for the classification of finite groups is exposed. A long chapter is dedicated to the action of a group on a set and to the permutations, both under the algebraic and combinatorial aspects, with references to the theory of equations. Some questions of a logical nature are also considered, such as the decidability of the word problem for certain classes of groups. An essential aspect of the book is the presence of a great variety of exercises, about 400, mostly solved.
: Mathematics and Statistics, Algebra, Group Theory and Generalizations, Commutative Rings and Algebras, Gruppi, Permutazioni, Rappresentazioni,