Free $\mathcal{A}_4$-actions on products of spheres

• Date: 2013
• Author Affiliations: Z. Blaszczyk — Faculty of Mathematics and Computer Science Nicolaus Copernicus University
• Keywords: keywords
• Main Author: Blaszczyk, Z.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/277
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

We summarize what is known about free actions of $\mathcal{A}_4$, the alternating group on four letters, on products of spheres. New results are also included: in particular, we prove that $\mathcal{A}_4$ acts freely on $S_n \times S_n \times S_n$ if and only if $n = 1, 3, 7$.