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DeadWolfe
- 457
- 1
I've always wondered, and I can't seem to find out...
A torsion group is a mathematical concept that refers to a group where every element has finite order. This means that when an element is combined with itself a certain number of times, it will eventually result in the identity element (an element that does not change the value of other elements when combined with them).
Torsion groups are different from other groups because they have a finite number of elements and their elements have finite order. In contrast, other groups may have infinite elements or elements with infinite order.
The name "torsion group" comes from the word "torsion," which means the twisting force of an object. In this context, the elements of a torsion group can be seen as being twisted or rotated a finite number of times to reach the identity element.
Some examples of torsion groups include finite cyclic groups, where the elements are generated by a single element with finite order, and finite abelian groups, where the elements can be rearranged in a way that they all have finite order.
Torsion groups have important applications in various fields such as number theory, algebraic geometry, and topology. They also provide a fundamental understanding of finite structures and symmetry, which has implications in physics and other sciences.