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- Title
ON CLOSED SUBGROUPS ASSOCIATED WITH INVOLUTIONS.
- Authors
Cánovas, J. S.; Bas, A. Linero; López, G. Soler
- Abstract
Given an involution f on (0, ∞), we prove that the set C(f) ≔ {흀 > 0 : 흀f is an involution} is a closed multiplicative subgroup of (0, ∞) and therefore C(f) is {1}, (0, ∞) or 흀&#x 2124 = {흀 n : n &#xicin; ℤ} for some 흀 > 0 , 흀 ≠ 1. Moreover, we provide examples of involutions possessing each one of the above types as the set C(f) and prove that the unique involutions f such that C(f) = (0, ∞) are f(x) = xc̱, c > 0.
- Subjects
GROUP theory; RINGS with involution; FUNCTIONAL analysis; FUNCTIONAL equations; DIFFERENCE equations
- Publication
Real Analysis Exchange, 2008, Vol 33, Issue 2, p395
- ISSN
0147-1937
- Publication type
Article