Yup, exactly. Slightly clearer explanation to anyone reading these comments:

Imagine there was only one unfaithful husband. The wife knows that there aren't any other cheaters, yet someone said there are. Only conclusion: her husband is unfaithful! So she kills him that night.

Now imagine if there were 2 unfaithful husbands. Take one of the unlucky women. She knows that there is one other unfaithful husband, and knows that her own husband is either faithful or unfaithful. Assuming he is faithful, the other woman will kill her husband that night. However, that doesn't happen so she concludes that her husband must be unfaithful and so kills him on the second night. The other woman uses the same logic and arrives at the same conclusion so both cheating husbands get killed that night.

Now imagine 3 unfaithful husbands. One wife knows that there are 2 other cheating husbands, so concludes that they must die on the second night. However this doesn't happen so she concludes that her husband must be cheating so kills him on the 3rd night. The other women use the same logic so all unfaithful husbands die on the 3rd night.

The exact same logic applies to any number n: If there are n cheating husbands, one wife knows about (n-1) of them so concludes they must be killed on the (n-1)th night. But when this doesn't happen she concludes her husband must be unfaithful and kills him on the nth night

Therefore, if there are n unfaithful husbands, they will all be killed on the nth night. As they were all killed on the 28th night there must have been n unfaithful husbands

This concept of proving stuff by assuming it's true for a similar but smaller situation is a thing in maths and is called proof by induction.

Now here's something extra to think about: What new piece of information did the person who said there were unfaithful husbands give? Surely they all knew that there were unfaithful husbands?

Answer going here if no one gets it in the next hour