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CONJUGACY CLASSES OF INVOLUTIONS IN THE GROUP OF HOMEOMORPHISMS OF THE RATIONAL NUMBERS

Name: CONJUGACY CLASSES OF INVOLUTIONS IN THE GROUP OF HOMEOMORPHISMS OF THE RATIONAL NUMBERS
Creator: Peter V. Bruyns
Keywords: 0101 mathematics, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 2001 English Publisher:Informa UK LimitedJournal:Quaestiones Mathematicae, volume 24, pages 237-246 (issn: 1607-3606, eissn: 1727-933X,

Authors: Peter V. Bruyns;

doi: 10.1080/16073606.2001.9639212

CONJUGACY CLASSES OF INVOLUTIONS IN THE GROUP OF HOMEOMORPHISMS OF THE RATIONAL NUMBERS

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Abstract

Let X be the set of real rational numbers Q with the topology induced by the usual topology on R and let AutX be the set of functions f : X → X which are homeomorphisms with respect to this topology. The set AutX is a group with respect to composition of functions. Let ƒ ∈ AutX be an involution whose fixed point set has derived set with n elements. It is shown that there are n + 2 conjugacy classes of such elements. Mathematics Subject Classification (1991): 20B22 Keywords: conjugacy classes, rational numbers, involutions, fixed point sets, multiply transitive finite groups, composition, fixed point Quaestiones Mathematicae 24(2) 2001, 237-246

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University of Cape Town
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