Google is currently testing a new domain registration service called Google Domains. Google is very early in the testing process for the new service and Google Domains is reportedly an invite only beta service for now. People familiar with the product say that Google has no plans to provide web hosting.
Once Google Domains launches to all users it will support the buying and selling of domain names. Each domain sold by Google will support up to 100 email addresses and up to 100 customized sub-domains.
One of the things that sets Google Domains apart from other registrars is that Google doesn't plan to charge extra to register the domain privately. Customers who register domains with Google will also get to use Google DNS servers.