I have been given all the privilages from my faction to perform an arrest and execution of a certain individual. Now, .... he is in our territory, ain't leaven, I can arrest him all live-long-day, but I do not see an option to execute, just release. I do have a weapon (knife) but, ... am I missing something here? Need to perform this quickly, my kindly banter of just telling him I'm wrestling is not going to hold much longer.

All I can think of is because you are currently travelling, if this does not help, please report this as a bug in the bug tracker.

Is he under arrest by someone else?

Hal: from what I undestand from his post he can arrest but can't execute.

Zao Nephalem: Maybe it's NPC and not PC. You can't execute NPCs.

Oh, duh, my bad. Misread it.

Is there a death warrant?

yes, there is a death warrent (so i've been told by the leader of the faction Raptor Pirates). We are both raptors, I can arrest, but then there is no option for execute, just release. I am on my ship (not raptors, privately owned) and in hyperspace. What am I not doing correctly?

It's probably the fact that you are in Hyperspace, which isn't controlled by anyone, not even the Galactic Government (although you're currently using IF A/E, which shouldn't be affected by the location rules of OOF A/E).
Try dropping out of HS into a location controlled by the Raptor Pirates and try again, if it still doesn't work then, report it to the bug tracker.

got it, will do .... in 3 days. Not dropping out of HS, last time, .... I got fried!