Steenrod closed parameter ideals in the mod-2 cohomology of A4 and SO(3)

Abstract

In this paper, we classify the parameter ideals in $H^{⁎}(B{A}_4;F_2)$ and in the Dickson algebra $H^{⁎}\left(B\mathrm{SO}\right(3);F_2)$ that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions $n,m$ for which $A_4$ (and $\mathrm{SO}\left(3\right)$) can act freely on $S^n\times S^m$.