AMS Chelsea Publishing 1956; 308 pp; hardcover Volume: 109 Reprint/Revision History: reprinted 1960; first AMS printing 2003 ISBN10: 0821834770 ISBN13: 9780821834770 List Price: US$44 Member Price: US$39.60 Order Code: CHEL/109.H
 Translated from the second Russian edition and with added notes by K.A. Hirsch. Teoriya Grupp by Kurosh was widely acclaimed, in its first edition, as the first modern text on the general theory of groups, with the major emphasis on infinite groups. The decade that followed brought about a remarkable growth and maturity in the theory of groups, so that this second edition, in English translation, represents a complete rewriting of the first edition. The book can be used as a beginning text, the only requirement being some mathematical maturity and a knowledge of the elements of transfinite numbers. Many new sections were added to this second edition, and many old ones were completely revised: The theory of abelian groups was significantly revised; many significant additions were made to the section on the theory of free groups and free products; an entire chapter is devoted to group extensions; and the deep changes in the theory of solvable and nilpotent groupsone of the large and rich branches of the theory of groupsare covered in this work. Each volume concludes with Editor's Notes and a Bibliography. Table of Contents Part Three. GroupTheoretical Constructions  Free Products and Free Groups: 9.33 Definition of a free product; 9.34 Subgroups of a free product; 9.35 Isomorphism of free decompositions. Free products with an amalgamated subgroup; 9.36 Subgroups of free groups; 9.37 Fully invariant subgroups of free groups. Identical relations
 Finitely Generated Groups: 10.38 General properties of finitely generated groups; 10.39 Gruško's theorem; 10.40 Gruško's theorem (conclusion); 10.41 Groups with a finite number of defining relations
 Direct Products. Lattices: 11.42 Preliminary remarks; 11.43 Lattices; 11.44 Modular and complete modular lattices; 11.45 Direct sums in complete modular lattices; 11.46 Further lemmas; 11.47 The fundamental theorem
 Extensions of Groups: 12.48 Factor systems; 12.49 Extensions of abelian groups. Cohomology groups; 12.50 Calculation of the second cohomology group; 12.51 Extensions of noncommutative groups; 12.52 Special cases
Part Four. Solvable and Nilpotent Groups  Finiteness Conditions, Sylow Subgroups, and Related Problems: 13.53 Finiteness conditions; 13.54 Sylow subgroups. The centers of \(p\)groups; 13.55 Local properties; 13.56 Normal and invariant systems
 Solvable Groups: 14.57 Solvable and generalized solvable groups; 14.58 Local theorems. Locally solvable groups; 14.59 Solvable groups with finiteness conditions; 14.60 Sylow \(\Pi\)subgroups of solvable groups; 14.61 Finite semisimple groups
 Nilpotent Groups: 15.62 Nilpotent and finite nilpotent groups; 15.63 Generalized nilpotent groups; 15.64 Connections with solvable groups. \(S\)groups. Finiteness conditions; 15.65 Complete nilpotent groups; 15.66 Groups with unique extraction of roots; 15.67 Locally nilpotent torsionfree groups
 Appendixes
 Bibliography
 Author Index
 Subject Index
