Cryptography and Vedic Mathematics are one of the fundamental branches of Mathematics and this book aims to serve as a reference book for the researchers. It can also be read with great interest by students of engineering. The material of the book has been arranged into sections spread out over seven chapters. Each chapter begins with a brief introduction which provides motivation and a keen desire to proceed with the material of the chapter. Several examples have been given for ready reference for solving problems in Cryptography and Vedic Mathematics. Remarks and notes at places and exercises have been given at the end of each section to increase the knowledge by applying previous results. The exercises have also been graded appropriately and followed by answers. Our sincere thanks are also due to the Publishers for undertaking the publication of the manuscript and bringing it timely in the market for the use of readers
The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
This book is based on the struggle of an ex Indian Military Intelligence Soldier against corruption. He lost everything in this war against corruption because of noncooperation by the corrupted system.
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