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On the non‐existence of free \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$ \mathcal {A}_d$\end{document} ‐actions on products of spheres
Author(s) -
Błaszczyk Zbigniew
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201000079
Subject(s) - mathematics , cohomology , prime (order theory) , combinatorics , integer (computer science) , group (periodic table) , spheres , mathematical physics , pure mathematics , physics , quantum mechanics , computer science , programming language , astronomy
We investigate the problem of existence of free alternating group actions on products of equidimensional spheres. Most notably, we prove that for a prime number p ≥ 7, the alternating group \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {A}_{p+1}$\end{document} cannot act freely on a finite‐dimensional CW‐complex with the integral cohomology ring isomorphic to that of ( S n ) p for any positive integer n . This extends previous results due to L. P. Plakhta.