# The Theory of Groups, Volume 2

###### Alexander G. Kurosh
Publisher:
American Mathematical Society/Chelsea
Publication Date:
1956
Number of Pages:
308
Format:
Hardcover
Edition:
2
Price:
37.00
ISBN:
0-8218-3477-0
Category:
Textbook
BLL Rating:

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

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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 Grusko's theorem; 10.40 Grusko'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 $\Pi$-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
* Subject Index