No, it is not. Trial version of Alfresco is able to create groups while its license is not in read-only mode (30 days from startup). You should go with admin user to Alfresco Share Administration Console, click Browse and then add a group clicking in the + symbol. Then, you may add the available users (create them previously if not) to the group.
As I had suspected. I have logged in both as myself and as my admin user and it makes exactly no difference. The same thing happens... or doesn't happen. I go into Admin Tools > Groups > Browse > + and then I enter a group name and a group title and I hit "Create Group" or "Create and Create Another" and the form does not submit. The groups are not created, the page does not reload or take me back to the list of groups. It does absolutely nothing. I have tried it in IE, Firefox, and Chrome under both accounts.
I suppose that you are adding a (non existing) identifier and display name when creating the group. If you see some of the fields in pink, you are trying with a non valid name (ex. with a slash / in the name or a dot or a space as the last character).
Finally, which version of Alfresco are you using ? is there any JS error in your web page when submitting the form ? is there any ERROR in your Alfresco logs ?
I have the same issue. A freshly provisioned cloud based trial instance does not allow me to create groups. It doesn't matter whether I try from behind, or a different machine in front of the corporate firewall, on Chrome, Firefox or IE, or what I type in the two required fields, clicking either the 'Create Group' or 'Create and Create Again' buttons has zero effect. No error, no change. Its like the buttons aren't registering that they are being clicked. I have definitely confirmed that the values in the Identifier and Display Name fields are unique and not already used (I've tried dozens of values - and neither were showing as highlighted in pink).