Elementary abelian p-groups are the only finite groups with the Borsuk-Ulam property

被引：0
|
作者：
Nagasaki, Ikumitsu [1 ]
机构：
[1] Kyoto Prefectural Univ Med, Dept Math, Sakyo Ku, 1-5 Shimogamo,Hangi Cho, Kyoto 6060823, Japan
来源：
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2019年 / 21卷 / 01期
关键词：
Borsuk-Ulam theorem; Borsuk-Ulam property; BU-group; representation sphere; equivariant map; COHOMOLOGY RINGS; THEOREM; EXISTENCE; MAPS;
D O I：
10.1007/s11784-018-0654-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is well known that the Borsuk-Ulam theorem holds for elementary abelian p-groups Cpk. 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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页数：14
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