By default you have a notification in the upper right corner if something new is posted in the group you are part of and a weekly digest of activities in the group.

However, you can manage the notifications and the digest and adapt them to your personal needs (e.g. if there a group or a discussion particularly important, you can set to receive an e-mail immediately, or on the contrary you prefer not to receive e-mail notifications and rely only on the upper right corner notifiers).

To do so, go to Account -> Settings. In the left column, you can choose to change the settings of your notifications in general, of the group notifications or of the digest.