The paper deals with the citation index and h-index, which are the main scientometric indices, currently used for evaluating the performance of scientists and university professors. The author indicates their main disadvantages and considers a number of illustra-tive examples. The study shows that the normalized citation index (taking into account the presence of co-authors) has a number of important advantages in comparison with other scientometric indices. The author proposes new indices — the maximum citation indices, which can be easily calculated, have a simple and clear interpretation and have a number of distinct advantages in comparison with the h-index.
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