What is the use of group theory in mathematics and how its applied on real life.Please give me a example......

Answer 1

Group theory is ultimately the analysis of symmetries. In mathematics, they will be used any time that there is a symmetry in a system. They also show up in algebraic topology (the fundamental group, and the homology groups of a space).

In real life, the symmetry group of a crystal or molecule directly impacts many of the physical properties of the crystal or material. For example, an x-ray diffraction pattern is affected by the group of symmetries of a crystal. Also, symmtries of a physical system often lead to conserved quantities in that system. For example, rotational symmetry is related to conservation of angular momentum and conservation of charge is related to 'guage symmteries'. For continuous symmetries, special groups called Lie groups are used. Each Lie group has a corresponding Lie algebra, which gives the conserved quantities of the system.

Answer 2

One application of group theory is on Quantic Physics