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Metals can form ionic bonds with non-metals. Non-metals can form bonds with each other covalently. Two metals cannot form compounds with each other.

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If you mean group x can form compounds with group y but not with atoms in group x. Then group x is the metals and group y is the non-metals.

The question is a little confusing as group one and group two mean somthing in chemistry. The chemistry generally group one and two is used to refer to two different types of metals called the alkali metalg and the alkaline earths. They are in these groups on the Periodic Table.

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