Can I Run a Thread Within a Thread in Java?

In Java I have the necessity of implementing a class that extends Thread within another similar class. Is that possible?

An example of what I am trying to do is the following (simplified) snippet:

// The first layer is a Thread
public class Consumer extends Thread {

    // Variables initialized correctly in the Creator
    private BufferManager BProducer = null;

    static class Mutex extends Object {}
    static private Mutex sharedMutex = null;


    public Consumer() {
        // Initialization of the thread
        sharedMutex = new Mutex();

        BProducer = new BProducer(sharedMutex);
        BProducer.start();
    }


    public void run() {

        int data = BProducer.getData();

        ///// .... other operations
    }


    ////// ...... some code

    // Also the second layer is a Thread
    private class BufferManager extends Thread {

        Mutex sharedMutex;
        int data;

        public BufferManager(Mutex sM) {
            sharedMutex = sM;
        }

        public int getData(Mutex sM) {
            int tempdata;
            synchronized(sharedMutex) {
                tempdata = data;
            }
            return tempdata;
        }

        public void run() {
            synchronized(sharedMutex) {
                data = getDataFromSource();
            }
            ///// .... other operations on the data
        }
    }
}

The second Thread is implemented directly inside the First one. Moreover I'd like to know if implementing a Mutex like that will work. If not, there's any better (standard) way to do it?

Thank you in advance.