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2007/2008 On Closed Subgroups Associated with Involutions
A. Linero Bas, J. S. Cánovas, G. Soler López
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Real Anal. Exchange 33(2): 395-404 (2007/2008).


Given an involution $f$ on $(0,\infty ),$ we prove that the set $\mathcal {C} (f) : = $ {$\lambda > 0 : \lambda f $ is an an involution} is a closed \multiplicative subgroup of $(0, \infty)$ and therefore $\mathcal{C}(F)$ is $\{1\}$, $% \intervalo$ or $\lambda ^{\mathbb{Z}}=\{\lambda ^{n}:n\in \mathbb{Z}\}$ for some $\lambda >0$, $\lambda \neq 1$. Moreover, we provide examples of involutions possessing each one of the above types as the set $\mathcal {C} (f) $ and prove that the unique involutions $f$ such that $\mathcal {C} (f) = (0,\infty)$ are $f(x)=\frac{c}{x},$ $c>0$.


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A. Linero Bas. J. S. Cánovas. G. Soler López. "On Closed Subgroups Associated with Involutions." Real Anal. Exchange 33 (2) 395 - 404, 2007/2008.


Published: 2007/2008
First available in Project Euclid: 18 December 2008

zbMATH: 1254.39010
MathSciNet: MR2458256

Primary: 39B22
Secondary: 26A18

Keywords: closed subgroups , difference and functional equations , involutions

Rights: Copyright © 2007 Michigan State University Press

Vol.33 • No. 2 • 2007/2008
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