This e-book, in a few experience, started to be written by means of the 1st writer in 1983, while not obligatory lectures on Abelian teams have been held on the Fac ulty of arithmetic and laptop Science,'Babes-Bolyai' collage in Cluj-Napoca, Romania. From 1992,these lectures have been prolonged to a twosemester electivecourse on abelian teams for undergraduate stu dents, via a twosemester direction at the comparable subject for graduate scholars in Algebra. all of the different authors attended those years of lectures and at the moment are Assistants to the Chair of Algebra of this Fac ulty. the 1st draft of this assortment, together with in basic terms routines solved by way of scholars as domestic works, the final ten years, had 160pages. We felt that there's a want for a publication comparable to this one, since it would offer a pleasant bridge among introductory Abelian workforce idea and extra complex learn difficulties. The ebook InfiniteAbelianGroups, released by way of LaszloFuchsin volumes 1970 and 1973 willwithout doubt final because the most vital consultant for abelian team theorists. Many workouts are chosen from this resource yet there are many different bibliographical goods (see the Bibliography) which have been utilized in order to make up this assortment. For many of the difficulties acknowledged, contemporary advancements also are given. however, there are many trouble-free effects (the so known as 'folklore') in Abelian staff conception whichdo now not look in any written fabric. it's also one function of this booklet to accomplish this hole.
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