Your message doesn't appear in your inbox if:

• you include your address in To or Cc.
• you send it to a mailing list that includes your address.

To prevent clutter, Gmail doesn't route messages that you send to your own alias (or to a group you belong to) to your inbox. You can find the message in Sent Mail or All Mail. (Cited from Gmail Help)

Only if you add the mailing list to your Gmail account and treat it as your alias does the messages sent to your group show up in your inbox. For more information, see:

• What happens to your Inbox or Sent labels when you send emails to mailing lists (available only in Japanese)
• How can I change my sender (From) address from my KUMail address to another?

For your information, Gmail treats duplicate emails as one message. See also:

• Some emails are missing