Final answer:
The cell responsible for the transmission of nerve impulses in the nervous system is the neuron, which generates and propagates electrical signals called action potentials.
Step-by-step explanation:
The type of cell responsible for the transmission of impulses through the nervous system is the neuron. Neurons are the structural and functional units of the nervous system, specialized in receiving stimuli and responding by generating electrical signals, known as action potentials. These action potentials are propagated along the axon of the neuron, allowing for rapid communication throughout the body. While other cells such as Schwann cells and oligodendrocytes provide supportive functions such as the production of myelin sheaths, which insulate axons to increase the speed of impulse conduction, they are not responsible for the transmission of nerve impulses themselves.