Abstract
It is well known that the Borsuk–Ulam theorem holds for elementary abelian p-groups \(C_p{}^k\). When the Borsuk–Ulam theorem holds for a finite group G, we say that G has the Borsuk–Ulam property or G is a BU-group. In this paper, we show that a non-abelian p-group of exponent p is not a BU-group, which leads to a complete classification of finite BU-groups, namely finite BU-groups are only elementary abelian p-groups.
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The author would like to thank the referee for carefully reading the manuscript and for giving valuable comments and suggestions.
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Nagasaki, I. Elementary abelian \(\varvec{p}\)-groups are the only finite groups with the Borsuk–Ulam property. J. Fixed Point Theory Appl. 21, 16 (2019). https://doi.org/10.1007/s11784-018-0654-y
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DOI: https://doi.org/10.1007/s11784-018-0654-y