Hi Alberto,
Yes, it is likely a problem with permissions.
Please let us know what you have installed and configured.
Is it AEM 6.1 Communities FP3? Or AEM 6.2 Communities?
See Creating Community Members.
See also enabling the tunnel service.
In AEM 6.2 there is a new Communities members and groups console for creating members and member groups on publish from author when the tunnel service is enabled, that will set permissions. The community member groups automatically created when using the community site creation wizard also set permissions.
The recommendation is to create a publish-side user group with the proper permissions and then assign publish-side users (members) to that group in order for them to inherit those permissions.
- JK