• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.653-659
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• 1997

In this paper, we extend the Gottlieb groups of a space to the Gottlieb groups of a map and show some properties of those groups. Especially, We show the 2nd Gottlieb group of a map is contained in the center of the homotopy group of the map and show $G_n(F) = \pi_n(f)$ for an H-map f between H-spaces. We also show the Gottlieb subgroups $G_n(A), G_n(X) and G_n(f)$ make a sequence if the map $f : A \to X$ has a right homotopy inverse.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.131-138
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• 1999

We introduce an extended Jiang subgroup $J(f,x_0,G)$ of the fundamental group of a transformation group as a generalization of the Jiang subgroup $J(f,x_0)$ and show some properties of this extended Jiang subgroup.