Atoms of one element react with atoms of other elements to change the number of electrons in the outermost shell. The objective of the reactions is to achieve a stable configuration which is that of a noble gas.Elements of the same group have the same kind of electronic configuration. The number of electrons in the outermost shell is the same. So the elements have to gain or lose the same number of electrons. This makes their properties similar.For example elements in the alkali metal group have one extra electron in their outermost shell. If this electron is lost they form an ion with a single positive charge and the electronic configuration changes to that of a noble gas. So, you will notice that all elements of this group form compounds where they are positive ions with a single charge.

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They have similar properties because they have the same number of valence electrons. Valence electrons are the ones that are involved in chemical bonding. (valence electrons just mean electrons on the outermost shell)