Others have requested the ability to search for and view user profiles when users ask to join a group. However, we've not implemented any user search due to privacy concerns. We are currently working on adding a "description" property to the user profile. If the user allows this to be seen, we can expose this description to the group administrator when that user asks to join a group.
FYI, you can share items with everyone or share them with groups. You can't share items with individual users.
Mike
ArcGIS Online team