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A note on the converse of the Lefschetz theorem for G-maps

M. Izydorek, A. Vidal (1993)

Annales Polonici Mathematici

The purpose of this note is to prove the converse of the Lefschetz fixed point theorem (CLT) together with an equivariant version of the converse of the Lefschetz deformation theorem (CDT) in the category of finite G-simplicial complexes, where G is a finite group.

Centralizers of gap groups

Toshio Sumi (2014)

Fundamenta Mathematicae

A finite group G is called a gap group if there exists an ℝG-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.

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