generalship

1. The position or office of a general.

   the office and authority of a general

2. The term of office of a military general.

   George Washington's generalship was marked by both amazing victories and stunning blunders, neither of which would have happened to someone with more formal officer training.

   the leadership ability of a military general

3. The skills or performance of a good general; military leadership, strategy.

4. By extension, leadership, good management.

   Under my generalship my fine troop of brats picked up every scrap of litter in that lot.

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