Group theory is abstract algebraic knowledge, which is difficult and abstract. Relatively speaking, group theory is much more difficult. Linear algebra also has some concrete and understandable contents such as matrices and linear equations, while the contents of group theory are mostly abstract mathematical structures, which require more imagination.

Application of group theory

Group theory is widely used in mathematics, which usually reflects the internal symmetry of some structures in the form of automorphism groups. The internal symmetry of a structure usually coexists with an invariant property. If there are invariants in a class of operations, the combination and invariants of these operations are collectively called symmetric groups.

Abel group extended several other abstract set research structures, such as rings, fields and modules. In algebraic topology, groups are used to describe the invariant properties in topological space transformation, such as basic groups and transmissive groups.

The concept of Lie group plays an important role in differential equations and manifolds. Because Lie group combines group theory with analytical mathematics, it can well describe the symmetry in the structure of analytical mathematics. This group of analysis is also called harmonic analysis. In combinatorial mathematics, commutative groups and group actions are often used to simplify the calculation of elements in some sets.