Yes, generally when you rez an item out it will be set to the same group you have active(but there are settings in some browsers that can force objects to always be rezzed under the land group). Also when you right click an object and select Edit, the screen that comes up shows about halfway down 'Group' and you can change that by clicking the spanner icon if you need to. Whatever group is shows for that item, your active group (Comms menu then Group or Ctrl Shift G) must be set to the same.
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