What is a key element required to establish common law conspiracy?

To establish common law conspiracy, a critical element is the agreement to commit an unlawful purpose. This means that the parties involved must have the intention to engage in conduct that is criminal or otherwise prohibited by law. The focus of common law conspiracy is on the agreement itself rather than the act that follows; thus, the mere agreement to achieve an unlawful end is sufficient to constitute a conspiracy, even if the crime is not ultimately carried out.

In this context, the other options do not meet the necessary requirements for a conspiracy. A valid contract is not a prerequisite for conspiracy, as the agreement can be informal and does not have to meet contract law standards. Agreement to accomplish a lawful purpose does not qualify, as conspiracy specifically requires an intention to pursue an illegal objective. Lastly, conspiracy does not have to involve public action; it can be a private agreement among individuals. Therefore, the essence of conspiracy lies in the intention to pursue an unlawful purpose, making it the correct key element in establishing common law conspiracy.