Introduction to Group Theory

Targeted at undergraduate mathematics students, this book aims to cover courses in group theory. Based on lectures in group theory, it includes many illustrations and examples, numerous solved exercises and detailed proofs of theorems. The book acts as a guide to teachers and is also useful to graduate students. The book discusses major topics in group theory such as groups and subgroups, binary operations, fundamental algebraic structure of groups, symmetric groups, cyclic groups, normal subgroups, quotient groups, homomorphisms, isomorphisms, direct product of groups, simple groups, set on a group, Sylow's theorem, finite group, Abelian groups and non-isomorphic Abelian groups.

Groups and subgroups.- Normal subgroups.- Finite groups.- Series groups.

Ahmed Ayache is Professor of Mathematics at the University of Bahrain, since 2013. Earlier, he was Dean of the Faculty of Science and Professor of Mathematics, the University of Sana’a, Yemen, respectively; Assistant Lecturer, the University of Aix–Marseille III, France, until 2013. With more than 54 articles in commutative algebra published, he has refereed numerous manuscripts in commutative algebra and published 2 books in mathematics (in Arabic language). A recipient of the Aden Prize 2000 in Fundamental Sciences, he has participated and organized numerous conferences and workshops and collaborated with other mathematical laboratories in France, the U.S.A., Tunisia, Qatar, and Saudi Arabia. His research areas are commutative algebra, rings theory, groups theory and fields theory. He earned his PhD in commutative rings from the University of Aix–Marseille III, France, in 1991; MS.c. in fields theory and B.Sc. in mathematics from the University of Aix–Marseille I, France, in respectively 1986 and 1985.

Khalid Amin is Associate Professor of Mathematics at the University of Bahrain, since 2013. Earlier, he was Associate Professor and Head of Mathematics at the University of Bahrain, until 2013. Nominated as one of the best researchers at the College of Science, during the academic year 1998–1999, and Member of several professional societies and committees, he has introduced a new program leading to a degree in Actuarial Science at the Department of Mathematics with the cooperation of the College of Information Science and College of Business Administration. He has examined several master theses, published several articles, refereed numerous manuscripts and participated in numerous conferences and workshops. His research area is group theory and its application in coding theory. He earned his Ph.D. in Mathematics from the University of Wales, Cardiff, U.K., in 1997; MS.c. in Mathematics from Michigan State University, East Lansing, Michigan, USA, in 1989; and B.Sc. from the University of Oregon, Eugene, Oregon, USA, in 1986.