(SI) Naš cilj je poiskati analog Wimanove 4(g+1) zgornje meje za velikost ciklične grupe, ki deluje na Riemannovi ploskvi roda g. Poleg tega načrtujemo posplošiti Oikawov izrek (1956), ki pove zgornjo mejo za grupo, ki deluje na ploskvi roda g z invariantnimi končnimi množicami določenega reda d>0. Nenazadnje, obravnavali bomo tudi naravo Weirstrassovih točk na grafu in poiskali način njihova izračunavanja. Prvi rezultati v tej smeri so bili dobljeni v člankih Bakera in Norinea in njunih študentov.
(EN) Our goal is to find an analogue of the Wiman 4(g+1) upper bound for the size of a cyclic group acting on a Riemann surface of genus g. In addition, we plan to generalize a theorem of Oikawa (1956), which gives an upper bound for a group acting on a surface of genus g with invariant finite sets of a certain order d>0. Finally, we will also consider the nature of Weirstrass points on a graph and find a way to compute them. First results in this direction were obtained in papers by Baker and Norine and their students.