Hi,

Is it possible to hide the "Edit Profile" button on the Profile page for a user group?

Joomla allow you to override Easy Profile profile page, so you can do everything you want to profile page. Unfortunately something like this require PHP and Joomla dev knowledges.

How to override Profile page
- Copy file from components/com_jsn/views/profile/tmpl/default.php to templates/your-template-folder/html/com_jsn/profile/default.php
- Edit new File: between lines 37 and 41 you will find the code that show edit profile button,

To do this you can add a code to check Joomla Usergroup (https://api.joomla.org/cms-3/classes/JUser.html#method_getAuthorisedGroups) or Access Level (https://api.joomla.org/cms-3/classes/JUser.html#method_getAuthorisedViewLevels)

Sorry, missing a part of reply

if I create a usergroup "A" and when a user exists in that usergroup they cannot edit the profile?

Sorry this is not possible with a simple way (hide edit profile button does not remove ability and permission to edit own profile).
personally,I should do this with one system plugin, but this way is not so simple