What is my hostname for Gmail outgoing mail server?
If you check Gmail's settings, under "Use your own email server," you will see a hostname.
Does that mean I should always use the same hostname for all outgoing emails (or is it for just my user account)? My concern is that if I send an email to someone outside of Google Apps using the correct hostname, and they don't have access to my app, will the address not work? If so, how does Google make it work on their servers? As always: everything that Google does has a very solid security track record. They have documented these practices on their website, but the general practice is this: If you are going to send e-mails through Google servers, then you should use the SMTP servers that Google provides as those are the ones that handle spam filtering and other important services that need to be applied to the e-mail. In your case, since you are sending e-mails through their Apps for business, you need to use the smtp servers listed on the Apps for Business page. The fact that these servers support POP3 is important because those are the protocols that are used by most mail clients. If you were sending mail via IMAP, you would use the same addresses that you use to connect to your IMAP server, but for most people, this will be the same address that is set up to use SMTP, which means that you should follow the steps in this FAQ, which explains how to configure the correct addresses on multiple smtp servers.
In your case, since you are sending mail through Apps for Business and using the smtp servers provided in that service, that is where you should configure your outgoing addresses. The reason that they provide the address "googlegroups.com" is because it is the official domain for GApps for Business. So even though the name you are using is google.com, it is the same address. In your configuration, you should make sure that you configure the addresses using the address "apps.com", and if you need to send mail to someone who isn't on the Apps for Business list, then you just configure that address using their normal mail address.
How do I find my Gmail SMTP host?
I have several domains that are hosted under one Google Apps account (). I have used the smarthost setting for a domain to be mysmtp.com with both port 25 and 80. In most cases, this is enough for me to be able to send emails from my account.
However, my main email account is at gmail.com, and I want to send emails from that address too. I would prefer not to use a third party mail server just to send gmail emails.
How do I find which server I should use as my Gmail SMTP host? Your Gmail-account is being handled by Google Mail and not by the app you use. When you use Gmail for sending/receiving mails you are using Gmail's servers to relay all emails over a secure connection to other servers. The mails are stored on GMail's datacenters, Google Apps uses these datacenters for all accounts using their services, no "outside" datacenters have access to this data. Google Apps has the smarthost setup for your domains if these can be found, but you must register the smarthost in the settings of your account.
If you want to receive mails via GMail, you need a GMail-address on a GMail-account. This GMail account is your personal account that will receive your mail, you don't need a domain name on this account.
If you set the smarthost to something other than google.com (or your own mail servers), the mails are send/received over a connection to your gmail-account. You can send an email without any special smarthost settings if you have the account configured in Gmail already (ie when you created it, not after).
When creating your mail-address/account you will find that it says "send mail from here", but unless you make that setting there is no way to send mails from another provider or a domain other than google.com - it's a "send mail from where GMail delivers mail from".
There are more info available in the related questions already asked: How to set an email address as smarthost in gmail? What is the difference between using a Gmail server as smarthost (on my account) vs. My regular account?
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