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.
Author(s): A. G. Kurosh
Edition: 2nd
Publisher: Chelsea Pub. Co.
Year: 1960
Language: English
Pages: C, 308
Part Three. Group-Theoretical 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 non-commutative 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 Π-subgroups of solvable groups; 14.61 Finite semi-simple 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 torsion-free groups
Appendixes
Bibliography
Author Index
