In Cognos 'group' is used to suppress the duplicate values. And 'associate' is used to suppress the values if it is a one-one relationship.
Both Group and Association eliminate duplicates in a column. But we cannot use the Association alone. It should have one to one relationship with the grouped column.
Using association is a performance enhancement technique. A group is used to eliminate the duplicates in data, whereas Association is used to hire or suppress the values in 1 to 1 relation.