Restrictions on free actions of the alternating group $A_6$ on products of spheres - Plakhta, L. P. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
We prove that the alternating group $A_6$ cannot freely act on $(S^n)^5$ We give an example of free action of the alternating group $A_4$ on $(S^n)^3$.