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The article link: https://www.bloomberg.com/news/articles/2019-06-03/alphabet-falls-to-lowest-in-five-months-as-doj-mulls-probe

Google parent Alphabet Inc., Facebook Inc. and Apple Inc. tumbled as the companies appear set to undergo U.S. antitrust probes after the Justice Department and the Federal Trade Commission agreed to split up oversight of technology giants.

I am having hard time understanding this sentence. Especially

"... as the companies appear set to undergo U.S. antitrust probes".

What does "appear set to" mean? Is set a verb or a noun? I don't know what kind of grammar it is to put 2 verbs together. Can someone explain it to me?

Also,

agreed to split up oversight of technology giants

I know what each individual word means, but when they combined together, I don't get what the FTC is trying to do with these technology giants. Do they want to supervise these companies or they are trying to split these companies into smaller ones?

One last thing, why does it say "Google parent" instead of "Google's parent"? Is it correct grammar?

... as the companies appear set to undergo U.S. antitrust probes.

"set to" means "prepared to" or "ready to" here, but with a strong implication that they are prepared because it is going to happen. So in effect, "set to" means "highly likely to".

Consider a parallel construction:

Jane appears ready to run the race.

I believe "ready" is a bare initiative form here, and "to run the race" is the object of "ready". Or perhaps it would be better to say that "appears ready" jointly form a phrasal verb, with "to run the race" as its object, and "Jane" as the subject. In that case, "appear set" is also a phrasal verb, with subject "the companies" and object "to undergo U.S. antitrust probes."

As to

... agreed to split up oversight of technology giants

This means that the US Federal Trade Commission (FTC) and the US Department of Justice (DOJ) have agreed to divide the task. According to the linked article:

... the FTC will oversee antitrust scrutiny into whether Facebook’s practices harm competition in the digital market. Reuters reported that the DOJ has been given jurisdiction over a potential probe of Apple.

So the split is between The FTC and the DOJ, not a prospective division of the companies into smaller parts.

"Google parent" is "headlinese" or "journalese". "Google's parent " would be more strictly correct, but in a news story, particularly in a headline or in an opening paragraph (or "lede" as it is known) brevity is of great value, and so two characters and one syllable are saved. This has been used often enough that the form "X parent, Y" for "Y, the parent of X" is in common use, especially in financial journalism. Often the parent company is the one legally involved in some action, but the subsidiary is far better known, as is the case here: Google is much better known than Alphabet. The form "X parent, Y" allows the emphasis to be put on X, the well-known name.

The question did not ask about it, but some may be confused by the use of "tumbled" in the opening sentence of the article. This means that the stock price fell suddenly and significantly.

Google parent Alphabet Inc., Facebook Inc. and Apple Inc. tumbled as the companies appear set to undergo U.S. antitrust probes after the Justice Department and the Federal Trade Commission agreed to split up oversight of technology giants.

1) Google parent Alphabet Inc., Facebook Inc. and Apple Inc.=those three companies

2) tumbled = the value of their shares on the stock market fell

3) appear set to undergo=seem to be ready or prepared for: to be set for

4) antitrust probes=antitrust is anti-monopoly, basically. The law is the anti-trust law, anti-monopoly law. probes=investigations of them by the Dept. of Justice and the FTC

5) oversight: that is a function in US government parlance. The FTC has oversight over certain matters, like making sure there are no monopolistic activities. To have oversight=to be in charge of overseeing or making sure organizations or companies behave properly.

6) to split up oversight=to share it, divide it into two parts; each authority will take half of the work of investigating them. Neither will do the work alone.

6) In financial news publications, they often do not use the possessive. They just do not. It's a style of financial writing.