Centralizers of gap groups

Volume 226 / 2014

Toshio Sumi Fundamenta Mathematicae 226 (2014), 101-121 MSC: Primary 57S17; Secondary 20C15. DOI: 10.4064/fm226-2-1


A finite group $G$ is called a gap group if there exists an $\mathbb {R}G$-module which has no large isotropy groups except at zero and satisfies the gap condition. The gap condition facilitates the process of equivariant surgery. Many groups are gap groups and also many groups are not. In this paper, we clarify the relation between a gap group and the structures of its centralizers. We show that a nonsolvable group which has a normal, odd prime power index proper subgroup is a gap group.


  • Toshio SumiFaculty of Arts and Science
    Kyushu University
    744 Motooka, Nishi-ku
    Fukuoka 819-0395, Japan

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