We have all had them haven't we? If you've done training you've had someone who's disruptive, possibly rude, pays no attention to you! If I'm totally honest, this type of participant used to upset me a fair bit when I first began training, there was me giving the performance of my life (!) And there was this smart alec trying to argue with me for arguments sake, chatting to the person next to them and generally being obnoxious! Luckily, I've only encountered two or three like this in my training lifetime but I feel the need to share you a nice little strategy to sort this blemish on a near perfect training life!
Firstly remember that these people are crying out for attention, it's not personal to you. Martin Luther king could be standing up there and they'd probably still try it on! They want to look good in front of the group, so try and do this:
Send the group on a break, and ask for a quick word with the offender. Say that you worried about the tension between you and the offender and apologise if you have done anything to upset them, but you don't want anything to come between the groups learning and if they could leave any "challenges" to the end/kerb their behaviour (add your own or delete as appropriate). This should do the trick, it's always worked for me, you've marked their card in a nice way and shown that you won't stand for it. Now, if the behaviour continues, which it shouldn't, try this:
During an exercise (you do exercises don't you??!) Take the offender to one side and ask them to leave. There is no point in risking the entire learning of the group due to one. Also ask them to explain to their manager why they have been asked to leave (Have a word with their manager afterward if at all possible). Never get yourself a reputation as a trainer who puts up with this sort of nonsense.