The PSG use two salutes:
The
Fist Pump salute, with their right hand, back of palm facing the recipient. With a fairly flat and laid back command structure in PSG, they usually refer to the party as "Sir!" or "Ma'am!". This is usually done between members of PSG and ISC Phoenix, plus multiple pumps may be done in very informal situations, along with requisite hooting or hollering.
The significance of this stems from the right hand of The Captain, which has The Grapple Stunner on it, from which
power comes. Power shall be thrust on those who abuse it. Luca didn't come up with this idea, or the fist pump - some of the men and women did and Luca let it stick.
In more formal situations, when they're out on field and representing themselves to the world, the men and women of PSG use the British salute with the thumb tucked in. Much more refined and dignified, and was chosen by Luca for that reason.
Meanwhile, on the ISC Phoenix itself, they rarely salute, but they do acknowledge each other by name.