How do I add a new group permission? How to add new group permissions? describes how add new group permissions when using the Drupal 7 version of the module.
function [mymodule]_group_permission() {
  return array(
    'schedule publishing of nodes' =&gt; array(
      'title' =&gt; t('Schedule content publication'),
      'description' =&gt; t('Allows users to set a start and end time for content publication'),
    ),
    'view scheduled content' =&gt; array(
      'title' =&gt; t('View scheduled content list'),
      'description' =&gt; t('Allows users to see all content which is scheduled.'),
    ),
  );
}

This does not appear to be the case in Drupal 8.
How can I add my own custom permissions to the group permissions screen, in Drupal 8?
I found the answer to this question here: https://www.drupal.org/project/group/issues/2959912

Create a .yml file, for example: my_module.group.permissions.yml

It should contain:

access group menu edit:
  title: 'Edit group menu'
  description: 'Allow users to edit the group menu'


First line is the permission itself.  I did this. Flushed cache, and my permissions now appear in Group module permissions screen under "My Module".