Sometimes a member of a group will be silent for a while, because he's busy working alone.

This isn't necessarily a bad thing. In fact, agreeing to work on sub-problems in parallel can be an effective way to make use of the members of the group.

However, if you're going to be working through something alone, make sure the rest of the group knows what you're doing:

A: I have an idea I want to try out, and
A: it will be quicker to work through it than explain it, okay?
B: Fine, let us know what you find out.

If you suspect that someone else is doing it, get confirmation if you can, and check back with him now and then if you haven't heard from him in a while:

B: A, do you have any thoughts about what we've been saying?
A: Um, I'm working on a different line of reasoning.
A: Give me another minute, okay? 
 .
 .
 .
B: Hey, A, how's your investigation going?  
B: Find anything we should know about?