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Suppose that there are many coins, and the coins are divided in two groups.

Based on this, I created two sentences below.

  1. The first group of coins is arranged in a ring, the second group of coins is arranged in a square.
  2. The coins in the first group are arranged in a ring, the coins in the second group are arranged in a square.

I think the second sentence is correct, but I am not sure the first sentence is correct.

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Both sentences are correct and natural. A fluent speaker might say or write either.

A "group of coins" is a single thing, and takes a singular verb form, even though it consists of multiple coins.

"The coins in the first group" describes multiple things, and takes a plural verb form.

Even though the underlying meaning is the same, the form of the object is not, and so the verb forms should agree.

When the verb "arrange" refers to the internal arrangement of a single thing that has sub-elements, such as a group of coins, a singular form is appropriate.

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