Which of the following statements is false?

The statement regarding activated M-Cdk triggering the onset of cytokinesis is false because M-Cdk primarily functions in promoting mitosis and the transition of the cell cycle into the M phase, where it regulates various processes necessary for cell division. Although M-Cdk does play a role in the processes leading to cytokinesis, it does not trigger cytokinesis directly. Instead, cytokinesis is the physical separation of the cytoplasm into two daughter cells, which is typically coordinated by a different set of signaling pathways and proteins that are activated after M-Cdk facilitates the onset of mitosis.

The other statements are accurate representations of cell cycle regulation. Activated G1-Cdks and G1/S-Cdks indeed help propel cells through the G1 phase and into the S phase, where DNA replication occurs. This transition is critical for ensuring that cells are ready to duplicate their genetic material. Additionally, S-Cdk is essential for initiating DNA replication, as it activates the proteins required for the unwinding of DNA and the assembly of replication machinery. Thus, the roles of G1-Cdks and S-Cdks in driving the cell cycle forward into DNA synthesis are correctly outlined in their respective statements.