If your role permits you to post events. There are a few things to keep in mind.

1) Pay close attention to the starting and ending dates and times.  In this version of Drupal the default values seem to be rather random. Perhaps it will be better in the future.  Just look at at each value before approving your post.

2) If you want the events to be visible to site visitors, you must check the  PUBLIC content box in the groups section. This is an exception to the norm which seems to apply to events.