Main Article Content
Conjugacy Classes of Involutions in the Group of Homeomorphisms of the Rational Numbers
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
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
