# Exercises in Group Theory

E. LyapinThe present book is a translation of E. S. Lyapin, A. Va. Aizenshtat, and M. M. Lesokhins Uprazhneniya po teorii grupp. I have departed somewhat from the original text in the following respects. I) I have used Roman letters to indicate sets and their elements, and Greek letters to indicate mappings of sets. The Russian text frequently adopts the opposite usage. 2) I have changed some of the terminology slightly in order to conform with present English usage (e.g., inverses instead of regular conjugates). 3) I have corrected a number of misprints which appeared in the original in addition to those corrections supplied by Professor Lesokhin. 4) The bibliography has been adapted for readers of English. 5) An index of all defined terms has been compiled (by Anita Zitarelli). 6) I have included a multiplication table for the symmetric group on four elements, which is a frequent source of examples andcounterex::Imples both in this book and in all of group theory. I would like to take this opportunity to thank the authors for their permission to publish this translation. Special thanks are extended to Professor Lesokhin for his errata list and for writing the Foreword to the English Edition. I am particularly indebted to Leo F. Boron, who read the entire manuscript and offered many valuable comments. Finally, to my unerring typists Sandra Rossman and Anita Zitarelli, I am sincerely grateful.

A group G is called divisible if every equation of the form nx = g, with n ∈ N* and g ∈ G, has a solution in G. If this holds only for those n which are powers of a fixed prime p, we obtain

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A group G is called divisible if every equation of the form nx = g, with n ∈ N* and g ∈ G, has a solution in G. If this holds only for those n which are powers of a fixed prime p, we obtain

E S Lyapin, A Ya Aizenshtat and M M Lesokhin published Exercises in group theory (Russian) in 1967. Eugene Schenkman, himself the author of a famous group theory textbook, has given the following translation of the chapter and section headings:

Exercises in Group Theory: Amazon.de: Lyapin, E ... Zum Hauptinhalt wechseln. Prime entdecken DE Hallo! Anmelden Konto und Listen Anmelden Konto und Listen Warenrücksendungen und Bestellungen Entdecken Sie Prime Einkaufswagen

Group Theory (Page 1) / Exercises / Math Is Fun … 18.03.2014 · Re: Group Theory The greatest tool in the mathematician's tool chest is abstraction. I cannot count all the times when I've done some long, horrific calculation or proof, and some time later came across an abstraction that made the whole thing almost trivial.

The first draft of this collection, including only exercises solved by students as home works, the last ten years, had 160pages. We felt that there is a need for a book such as this one, because it would provide a nice bridge between introductory Abelian Group Theory and more advanced research problems. The book InfiniteAbelianGroups, published Exercises in Group Theory: Amazon.es: Lyapin, …