Hi Dana, yes you are correct it is the group, a nice way to check is via a periodic table, elements that are similar are "grouped" vertically, and those pesky periods are horizontal.
Quatum levels deal with spin of the electron, and oxidation or oxidized elements are positive with losing their crazy electrons.
The reason for the similarity in a group is due the outer shell with valence electrons. So in Group 1A, which contains H, Li, Na, K, Rb, Cs, Fr, they have one valence electron or some may have similar physical properties as well ex. Noble Gases.
Hope that helps ya.