- #1
Konte
- 90
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Hi everybody,
I have a question: is an abelian group can be isomorphic to a non-abelian group?
Thank you everybody.
I have a question: is an abelian group can be isomorphic to a non-abelian group?
Thank you everybody.
DrDu said:In a non-abelian group, there are at least two elements A and B so that A*B=C but B*A=D with different D and C. this is not possible in an abelian group, so the two groups can also not be isomorphic.
Group theory is a mathematical framework used in physics to study the symmetries and invariances of physical systems. It involves the study of groups, which are sets of mathematical elements that can be combined or transformed in specific ways while still maintaining the same structure.
Group theory is used to understand the fundamental laws of nature and the behavior of physical systems. It is applied in various areas of physics, such as quantum mechanics, particle physics, and solid state physics, to study the symmetries and conservation laws of these systems.
In physics, a symmetry refers to a transformation that leaves a physical system unchanged. This could be a spatial or temporal transformation, such as rotation, translation, or time reversal, or it could be a transformation of the system's internal properties, such as charge or spin. Symmetries play a crucial role in determining the behavior and properties of physical systems.
Group theory provides a powerful tool for analyzing the symmetries and invariances of physical systems. By identifying the symmetries present in a system, we can make predictions about its behavior and properties. Group theory also helps in classifying different physical systems and understanding the relationships between them.
One example of group theory in physics is the study of rotational symmetries in quantum mechanics. The group of rotations in three-dimensional space, known as the group SO(3), plays a crucial role in understanding the behavior of particles with spin. By applying group theory, we can predict the energy levels and allowed transitions of these particles, as well as their behavior under different transformations.