Symbolism, Imagery, Allegory
Fulgor has some issues with his manhood. He hates it that kids who are younger than him get to boss him around, and he is also seriously worried about whether or not he's a coward. That might be why he whips out his, well, whip every time he gets around his brosef Pedro: "He used the butt of his whip to knock at Pedro Páramo's door" (19.1).
The guy isn't even whipping things. He's just taking out his whip as if to say "Hey guys. I have this here whip. Check it out."
Yeah, you know where we're going with this: Fulgor's whip is a phallic symbol, something that symbolizes (if only to Fulgor) a sense of power and manliness. He carries it like a good charm when he has to go meet with Pedro: "Fulgor followed with long strides, slapping his whip against his leg. He'll soon learn that I'm the man who knows what's what" (19.4).
When Fulgor says that he is going to show Pedro that he's "the man," he's holding onto the whip as though it were a lucky charm. Hey, it must be hard to be any man besides Pedro in the town of Comala—you'd be perpetually made aware of the fact that you were not the top dog or alpha male.