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On One-parameter Subgroups in Finite Dimensional Locally Compact Group with No Small Subgroups

Published online by Cambridge University Press:  22 January 2016

Masatake Kuranishi
Masatake Kuranishi*
Affiliation:
Mathematical Institute, Nagoya University
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Let G be a locally compact topological group and let U be a neighborhood of the identity in G. A curve g(λ) (|λ| ≦ 1) in G, which satisfies the conditions,

g(s)g(t) = g(s + t) (|s|, |f|, |s + t| ≦ l),

is called a one-parameter subgroup of G. If there exists a neighborhood U1 of the identity in G such that for every element x of U1 there exists a unique one-parameter subgroup g(λ) which is contained in U and g(1) =x, we shall call, for the sake of simplicity, that U has the property (S). It is well known that the neighborhoods of the identity in a Lie group have the property (S). More generally it is proved that if G is finite dimensional, locally connected, and is without small subgroups, G has the same property. In this note, these theorems will be generalized to the case when G is unite dimensional and without small subgroups.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 4 , June 1952 , pp. 89 - 96
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1952

References

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