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Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography. The early history of group theory dates from the 19th century.
Why is group theory important? Broadly speaking, group theory is the study of symmetry. When we are dealing with an object that appears symmetric, group theory can help with the analysis. We apply the label symmetric to anything which stays invariant under some transformations.
Group theory is the study of groups. Groups are sets equipped with an operation (like multiplication, addition, or composition) that satisfies certain basic properties. As the building blocks of abstract algebra, groups are so general and fundamental that they arise in nearly every branch of mathematics and the sciences.
Jun 11, 2024 · group theory, in modern algebra, the study of groups, which are systems consisting of a set of elements and a binary operation that can be applied to two elements of the set, which together satisfy certain axioms.
- The Editors of Encyclopaedia Britannica
Group theory is the study of symmetry. When an object appears symmetric, group theory can help us study it. We apply the label \symmetric" to anything that is invariant under some transformations. This can apply to geometric gures (a circle is highly symmetric, being invariant under all rotations), but also to algebraic objects like functions ...
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Why is group theory important? Broadly speaking, group theory is the study of symmetry. When we are dealing with an object that appears symmetric, group theory can help with the analysis. We apply the label symmetric to anything that stays invariant under some transformations.
Group theory, and abstract algebra more generally, is about ideas like this; by prioritizing abstract symmetries and patterns associated to objects over the objects themselves, unexpected connections are sometimes revealed.
