Vermani L.R. An Elementary Approach to Homological Algebra

Chapman & HALL/CRC.: CRC Press LLC. 2003. - 316p. - ISBN: 1-58488-400-2, English.Homological algebra arose from many sources in Algebra and Topology. However, the subject appeared as a full-fledged subject in its own right in 1956 when the first book on the subject and still a masterpiece by H. Cartan and S. Eilenberg appeared. More books have appeared on the subject since then, notably by D.G.Northcott. S. MacLane. P.J.Hilton and U. Stammbach. ,T.,T. Rotman. C. A. Wiebel. However, none of these could be adopted as a textbook for a student coming across the subject for the first time. The author felt this difficulty while teaching a one semester course on the subject at Kurukshetra University during the last, few years.
The students found it. hard in the absence of a suitable text book. The present text is a result of the lectures given at Kurukshetra during which time books by Northcott. Rotman and Hilton and Stammbach were freely used while lecturing. The material covered in the book may be adopted for a two semester course, while a one semester course could be based on the first seven chapters. The book shall also be useful for researchers who like to use the subject in their study. Complete detailed proofs are given to make the book easy for self study.
The book aims at giving just a basic course on the subject and is by no means exhaustive. Several important areas in the subject have not. even been touched upon.
The last chapter, as applications of homological methods, gives two purely group theoretic problems. One of these is a result, of Gasclmtz that, every non-Abelian finite p-group has an outer automorphism of p-power order and the other result, as shown by Magnus is that, a group having a free presentation with n + r generators and r relations which can also be generated by n elements is a free group of rank n.