Should the periodic table's groups be hyphenated? [closed]

In your example, I would consider group-IV to be a phrasal adjective, or compound modifier, and therefore use a hyphen, as recommended by many popular style guides.

When two words together serve as a modifier for another word, many style manuals recommend hyphenating them, as for example...

The built-up area of town...

A brightly-lit hallway...

Since this is related to chemistry, I checked the American Chemical Society's style manual, which does not specifically address phrasal adjectives, but does favor hyphenation for most modifiers.

However, if you're writing for a specific journal or publication, you may want to ask them what style guide they recommend.