#### ABOUT THE BOOK

This book for the student of semester-I of M.Sc. of Punjabi University Patiala; Topics of this book are:- Review of groups, subgroups, cosets, normal subgroups, quotient groups, homomorhisms and isomorphism theorems. Normal and subnormal series, Solvable groups, Nilpotent groups, Composition Series, Jordan-Holder theorem for groups. Group action, Stabilizer, orbit, Review of class equation, Permutation groups, cyclic decomposition, Alternating group A_(n,) Simplicity of A_(n,) Structure theory of groups, Fundamental theorem of finitely generated abelian groups, Invariants of a finite abelian group, Sylow's theorems, Groups of order P^2,pq. Review of rings and homorphism of rings, Ideals, Algebra of Ideals, Maximal and prime ideals, ideal in Quotient rings, Field of Quotients of integral Domain.

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