Özet:

Basic Applications on Surfaces Simeters Ggssdeliance Galan compact connected to a rotatable surface. If the group acts faithfully in gSüzer as a group of self-homeomorphisms that preserve the direction of GgS, then it is called GgSüzer, or GgS's a symmetrical group. Let’s show the set of G values in the form that will affect the GgSüzer with Gn. In this study, this aggregate was calculated for the groups (22GCC=×ppGCC=×p a single original number), 4,AA (alterne groups) and (simetric groups). Furthermore, a gx set of values in the form that will release the 4SGGgSüzer for these groups has been obtained. SOME APPLICATIONS ON SYMMETRIES OF SURFACES Let be a non-trivial finite group and GgΣdenote a compact connected orientable surface of g. If Gcts faithfully on gΣ group of orientation-preserving self-homeomorphisms of gΣ, e say that G acts on gΣot G is a symmetry group of gΣ. t (G)ν note the set of values of g r which Gcts on agSn this paper, we compute this set for the groups GC, (is an odd prime), I22C=×ppGCC=×p4,AA alternating groups and symmetric group. We also obtain the set 4S()Gx of g such that acts freely on GgΣfor these groups.

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