In my organisation, we moved from on-premises Exchange to Office 365 during March 2017, and we noticed that emails sent to the group were no longer received by the sender in their inbox. This was considered to be a problem since users were used to getting a copy of the email in their inbox.
This was the result of a feature update implemented by Microsoft in February 2017:
Therefore as a result of this change, the issue raised by David Eisen is no longer affecting users. If users wish to confirm that their email was sent and received by the group, then they can check their Sent Items, and also they can open the relevant Group folder within Outlook.
Microsoft is considering (as of April 2017) implementing a further enhancement to address negative feedback, which I assume means providing a configuration option for senders to also receive a copy in their inbox once more!