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In mathematics and abstract algebra , group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings , fields , and vector spaces , can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom , may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics , chemistry , and materials science.
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By Morton Hamermesh.
Theory of Groups and Its Application to Physical Problems is an introductory study of the theory of groups for persons with no easy access to an orthodox mathematical treatise on the subject. The aim is to provide an understanding of the method of applying group theory to various problems and appreciate the advantages thereof. It is hoped that this account of the theory of groups will serve a real need for physicists interested in the subject. The book opens with a discussion of the concept of groups.
Symmetries play an increasingly important role throughout mathematics, physics, chemistry, solid state physics, nuclear physics, particle physics, and other branches. Since Galois theory was proposed in , the years have witnessed fruitful applications of group theoretical methods. Earlier in the s, Weyl found the importance of group representations in modern physics. As a natural tool, the group theory helps us to understand the symmetry properties of a system and the nature of physical laws. There is also new development in applying the group theoretical approach to various fields. We invite investigators to contribute original research articles as well as review articles that will stimulate the applications of group theoretical approach in mathematics, physics, and chemical physics.
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