A cyclic subgroup is a subgroup generated by a single element, meaning that every element in the subgroup can be expressed as a power of that element. This concept is central to group theory, as cyclic subgroups can provide insights into the structure of the larger group they belong to. They are often characterized by their simplicity and can be finite or infinite, depending on the properties of the generating element.
congrats on reading the definition of cyclic subgroup. now let's actually learn it.