The email is sent to your user to validate their email ID and this is done via the plugin "User Validation by Email".
As you said that you want to make the user register on button click straight away and don't want them to validate the email ID then all you need to do is simply disable the "User Validation by Email" plugin.
While disabling the uservalidationbyemail plugin activates the new accounts immediately the problem is that it increases the risk of getting more spammers registering an account as they wouldn't even have to provide a valid email address anymore. To reduce the risk of spammers it's better to keep the email validation of new accounts enabled. Even more so I would suggest to use the Spam Login Filter plugin additonally to reduce the number of spam accounts created further (a 100% spam-free site is probably impossible to achieve but the Spam Login Filter plugin at least helps and if you register an account at StopForumSpam and report spammers who got through on your site you can prevent them from registering an account with the same credentials not only on your site but also on any other Elgg site using Spam Login Filter).
Just for clarification: is the "takes minutes to register" you are referring to the time necessary from clicking on the register button until you get the validation email or is it something connected with the Facebook Homepage plugin that takes longer for the registration to finish compared to the time necessary without using this plugin?
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