Definition of symmetric product in Milnor's paper

Question

I am currently reading Milnor's paper which discusses the group action on spheres without fixed point. At the second page of the paper, he denotes $$M^n*M^n$$ to be a symmetric product of a manifold. I was confused of what this means, as it does not adjust to any of the definition of the terms on Wikipedia. Any comments in appreciated.

Answer 1

It should mean $M*M = M\times M/ \sim$, where $(x, y) \sim (y, x)$. -- John Ma

To confirm that the answer by John Ma is correct, I looked up another paper which gives this definition of symmetric product just before citing the aforementioned Milnor's paper about it.