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In Maine, Republican Charlie Summers topped five others in the GOP primary and Cynthia Dill won the Democratic primary for the state’s open Senate seat. They will go up against former Gov. Angus King, an independent who is the front-runner to succeed retiring Sen. Olympia J. Snowe, a Republican.

Republicans say they believe Mr. King has struck a back-room deal to support Democrats should he be elected, and they are hoping to try to divide Democratic voters in the state.