Description
Book SynopsisA translation from the second Russian edition of ""Teoriya Grupp"". It covers the theory of abelian groups. It also covers the theory of free groups and free products; group extensions; and the deep changes in the theory of solvable and nilpotent groups.
Table of ContentsPart 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.
