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The word "temperance" tells you what problem these groups were considered. Temperance here refers to drinking alcoholic beverages. These groups were worried about excessive drinking.

If you mean the 5th problem of Hilbert it was: Are continuous groups automatically differential groups?

Some word endings for "problem" are problematic, problematize, and problematical.

What is a type of research that uses focus groups or small studies to get a "feel" for the problem.