Geodesic
On a Transformation Group
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 935-941

Voir la notice de l'article provenant de la source Cambridge University Press

0. Let Γ denote a group of real linear fractional transformations (the constants defining any element of Γ are real numbers); see (3, § 2, p. 10). Then it is known that Γ is discontinuous if and only if it is discrete (3, Theorem 2F, p. 13).Now Γ may also be regarded, equivalently, as a group of homeomorphisms of a disc D onto itself; and if Γ is discrete, then, except for elements of finite order, each element of Γ is either of type 1 or type 2 (see Definitions 0.1 and 0.2 below).We wish to generalize the result quoted above in purely topological terms. Thus, throughout this paper we denote by X a compact metric space with metric d, and by G a topological transformation group on X each element of which, except the identity e, is either of type 1 or type 2. Let L = {a ∈ X: g(a) = a for some g in G — e}, and . We assume furthermore that 0 is non-empty. 
Kaul, S. K. On a Transformation Group. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 935-941. doi: 10.4153/CJM-1969-102-7
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