Thank you for all that interesting info, kelan. I'm sure it will help me to understand this issue. Unfortunately at this point, I can't make the connection to my question. (All I know about XML is that it's a source code for webpages. I did not know that svg is an xml file format.)
By Z-Order (which I find in one of the Help menu tutorials, I think 'Basic'), I mean the order in which objects are stacked up. Here, I'll put up an example.

In this image, everything is all in the same regular layer. There is the grid of blue on top of a grid of purple, in the z-order. They are identical other than their color.
I want to lower all the blue squares with a red dot, below the purple squares. I have already lowered 6 of them (they are below the 6 numbered purple squares). So instead of moving them one at a time, I thought if I grouped them, I could lower them all in one click.
So all the blue squares with a red dot, plus the 6 that are already below purple squares, are in a group. I had to click Lower 5 times before the 1st blue square moved, revealing the purple square with the number "1". 2 more clicks, and the purple square with "2" is revealed. Then it took 4 clicks of the Lower button, to move the 3rd blue square below purple "3". Then it took 2 more clicks to get purple "4". Etc.
I'm pretty sure that the reason I have to click so many times, before something moves, illustrates your comment that each object occupies its own Z-Layer. And I suppose that's part of the answer to my question! Each object occupies one z-layer.
So in a group, there are as many Z-Layers as there are objects, right?
But those z layers aren't a group? Meaning that other objects can get between the z layers of grouped objects?
I still don't get how those purple squares can be between the blue squares' z layers.... Until now, I've thought of the z-order as something like sublayers, and expected they should behave like regular layers. So I still don't understand your comment:
The only thing groups do in regards to z-order is force all of the group members to appear together.
because the blue squares in my group are not appearing together. Some of them are below purple squares, and some are above. I expected that they should be either all above or all below the purple.
I know that in this case, I could use the Lower to bottom button, and move them all at once. And I may be able to manipulate things in my image, to allow me to do that. But the question is still nagging me, how some squares in the group can be below the purple squares, while some are still on top, and why they don't get lowered all at once.
Sorry if I seem dense -- it's really more like I don't have the right perspective to approach my question. I'm sure I'll get it, once I find the right approach.
Thanks for your help and patience
