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Luris
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Hi, I'm not finding group theory listed in any of the other math forums on physicsforums.com... so I'm wondering if it belongs here in the General Math forum or in another?
Group Theory is a branch of mathematics that studies the properties and structures of groups. A group is a set of elements that follow certain rules of operation, such as multiplication or composition, and has specific properties such as closure, associativity, and identity.
Group Theory has a wide range of applications in various fields, including physics, chemistry, computer science, and cryptography. It helps to understand the symmetry and structure of complex systems, and provides a powerful tool for solving problems in these fields.
Group Theory is closely related to symmetry because groups are used to describe and classify symmetries. In fact, the concept of a group was first introduced by mathematicians to study the symmetries of geometric figures.
Some common examples of groups include the integers under addition, the real numbers under multiplication, the set of all permutations of a finite set, and the symmetries of a regular polygon.
Group Theory has many practical applications, such as in cryptography where it is used to develop secure encryption algorithms. In physics, it is used to describe the symmetries of particles and their interactions. It is also used in chemistry to understand the structures and properties of molecules.