Asalamualiqum,my question is , I know a man who purposely denied marriage,to gain some benefits, by submitting a written statement on oath. What is the ruling of islam on this act ?

It is hard to understand your question please give some more explanation, Gaining benefits form what?

Divorce is allowed in Islam if that's what you mean.

https://www.thoughtco.com/steps-to-a...ivorce-2004442

Quote:

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If, after thoroughly evaluating your marriage, you find that there is no other option than divorce, there is no shame in proceeding to the next step. Allah gives divorce as an option because sometimes it is truly the best interest of all concerned. Nobody needs to remain in a situation that causes personal distress, pain, and suffering. In such cases, it is more merciful that you each go your separate ways, peacefully and amicably.

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Not sure what you mean by denying a marriage for benefit. If you can clarify that would be great.