Does the Lambda , AWS Active MQ support Message Groups ?

To answer my own question, the AcitveMQ Message Group is irrelevant as the documentation says

"The Lambda service limits the concurrency to one execution environment per queue." see https://aws.amazon.com/blogs/compute/using-amazon-mq-as-an-event-source-for-aws-lambda/

As such there will never be more than one lambda function being executed at one time as part of a synchronous call, as no no matter whether the Message Group is specified there will not be any opportunity to increase the amount of concurrent processing.