Fixed points in a transformation group

Abstract

In this paper, the following result is proved: "Let (X, T, ) be a transformation group, where X is a Peano continuum with an end point fixed under T. If the group T is one of the following two types: (1) It contains a subgroup R n such that G/R n is compact or (2) It contains a s subgroup Z-R n such that GI(Z-R n ) is compact, where Z is isomorphic to the discrete additive group of all integers, then T has another fixed point."