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hkhk
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hkhk
if G= Z4 x Z what would be the torsion group T(G)?
and what is the factor group of G/ T(G) ?
if G= Z4 x Z what would be the torsion group T(G)?
and what is the factor group of G/ T(G) ?
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A torsion group is a group in which every element has finite order, meaning that when an element is multiplied with itself multiple times, it eventually becomes the identity element.
A non-torsion group, also known as a torsion-free group, is a group in which no element has finite order. This means that when an element is multiplied with itself multiple times, it will never become the identity element.
A torsion subgroup is a subgroup of a torsion group in which all elements have finite order. This subgroup is also a torsion group itself and may or may not be equal to the original torsion group.
The torsion subgroup is closely related to the concept of finite order because it is a subgroup of a torsion group, meaning that all its elements have finite order. It is also possible for a group to have a torsion subgroup while not being a torsion group itself.
Studying torsion groups and subgroups is important in group theory and abstract algebra, as they provide insight into the structure and properties of groups. They also have applications in various fields such as cryptography, physics, and chemistry.