What phase is the period during the life of a cell between the end of mitosis and the synthesis of more genetic material?

Answer 1

The G0 phase (referred to the G zero phase) is a period in the cell cycle in which cells exist in a quiescent state. G0 phase is viewed as either an extended G1 phase, where the cell is neither dividing nor preparing to divide, or a distinct quiescent stage that occurs outside of the cell cycle. G0 is sometimes referred to as a "post-mitotic" state, since cells in G0 are in a non-dividing phase outside of the cell cycle. Some types of cells, such as nerve and heart muscle cells, become post-mitotic when they reach maturity (i.e., when they are terminally differentiated) but continue to perform their main functions for the rest of the organism's life. Multinucleated muscle cells that do not undergo cytokinesis are also often considered to be in the G0 stage. On occasion, a distinction in terms is made between a G0 cell and a 'post-mitotic' cell (e.g., heart muscle cells and neurons), which will never enter the G1 phase, whereas other G0 cells may.

Source: wikipedia.org

Answer 2

The phase you are referring to is called the G1 phase of the cell cycle. During this phase, the cell grows and prepares for DNA replication.