Wiktionary
a. Describing those Italian soldiers who chose to stay faithful to the Italian Crown and then-Army Commander http://en.wikipedia.org/wiki/Pietro%20Badoglio after http://en.wikipedia.org/wiki/September%208 http://en.wikipedia.org/wiki/1943, during World War II, as the Fascism regime fell in Italy and the Italian army was left without a lead as http://en.wikipedia.org/wiki/Victor%20Emmanuel%20III%20of%20Italy fled the country.
Usage examples of "badoglian".
There was talk about a Badoglian leader known as Mongo—a nickname, naturally, as was the custom then.
And Mongo also snapped to attention and introduced himself: Sergeant Major Rebaudengo, Royal Carabineers, commander of the Badoglian brigade Bettino Ricasoli, bronze medal.
It was said that on the evening of the battle the Badogliani had flung themselves at the enemy, shouting “Forward, Savoy!