Thanks for the reply Goran. I have tried that but I get the same error. For example, with this POST body:

POST https://xxxxx.service-now.com/api/x_xxxxx_xxxxxxxx/inbound

{
    "action": "insert",
    "type": "incident",
    "payload": {
        "correlation_id": "d87d1554-8386-45d5-9464-b4bb8f062a6d",
        "short_description": " Test__20180612_113606",
        "assignment_group": "MyTestGroup",
        "company": "Oltiva",
        "description": "This is a test SR",
        "impact": "1",
        "state": "1",
        "urgency": "2"
    }
}

I get the following response:

{
    "result": {
        "success": false,
        "message": "Invalid assignment_group: MyTestGroup"
    }
}

I can look up that assignment group by name using the following GET request:

https://xxxxx.service-now.com/api/now/table/sys_user_group?sysparm_query=name=MyTestGroup

Are there other considerations that might cause that error beyond supplying an invalid value for that property?