Abelian Groups

László Fuchs is the Evelyn and John G. Phillips Distinguished Professor Emeritus in Mathematics at Tulane University. He was awarded the Kossuth Prize in 1953 and is a foreign member of the Hungarian Academy of Sciences.

• Fundamentals.- Direct Sums.- Direct Sums of Cyclic Groups.- Divisibility and Injectivity.- Purity and Basic Subgroups.- Algebraically Compact Groups.- Homomorphism Groups.- Tensor and Torsion Products.- Groups of Extensions and Cotorsion Groups.- Torsion Groups.- p-Groups with Elements of Infinite Height.- Torsion-free Groups.- Torsion-free Groups of Infinite Rank.- Butler Groups.- Mixed Groups.- Endomorphism Rings.- Automorphism groups.- Groups in Rings and in Fields.

“This is an amazing, fairly comprehensive account of the present state of the theory of abelian groups. … I deem Abelian groups a ‘must have’ for any algebraist, especially those working with rings and modules.” (Manfred Dugas, Mathematical Reviews, December, 2016)