You can group controls, you can do clicking on the group button or using the group command.
When you select more than one control you can group them clicking on the group button. When you select a group, the label of the group button became ungroup and clicking on it you may ungroup items.
Moreover you can edit a group selecting it and clicking on edit group button.
If you prefer to always be able to modify items in a group, without clicking on edit group, you can click on select grouped button. This way you can always modify groups: use it with caution, because is easy to involuntary change a group.
You can do the same way with the command group. If you use just the command, without argument, you'll group the selected object, example:
If you use group command with a control list (every control separeted by the and word), you group the control in the list:
group field "Help" and image "Help Icon" and graphic "Outline"
You can know the name of the group containing an object using the owner property.
You can add object to a group with:
create objReference in group "groupName"
LiveCode you can create a background group that can be on every card. First create your button(s) select it (them) and press group in the toolbar. That will create a group. In the inspector for the group you then select Behave like a background. All new cards will have your button(s) automatically. If you already created a bunch of cards you can always add the group by selecting "Object => Place Group => " in the menu.
A group can exist without being placed on any card. If you set the CantDelete property to true of a group and delete the card of the group, in the Object menu you should see that the group is still available and was never deleted. But if you specifically try to delete the group itself, you won't be able to, at least not without a warning. Unplaced groups are handy for storing resources (usually images and icons) so they are always available and don't need to clutter up a card.
These are all properties of a group (help us to complete this list):