The primary structure responsible for hair growth is the follicle. Hair follicles are specialized structures in the skin that produce hair strands. Each follicle has a growth cycle, which includes stages of growth, rest, and shedding. Within the follicle, hair cells rapidly divide and mature, contributing to the formation of hair. The follicle houses the hair root and is embedded in the dermis, where it receives nourishment from blood vessels.
The dermal papilla, which is located at the base of the hair follicle, plays a supporting role by supplying nutrients and signaling hair growth, but the follicle itself is the structure where the actual hair growth takes place. The hair shaft, which is the visible part of the hair, does not have living cells; it is composed of dead keratinized cells. The sebaceous gland produces oil to lubricate the hair and skin but is not directly involved in the process of hair growth. Thus, the follicle is integral to the formation and growth of hair, making it the correct answer.