Abstract
Abstract In this paper, we prove that if 𝐺 is a group generated by elements of order two with the property that the product of any two such elements has order 1, 2, 3 or 5 with all possibilities occurring, then G ≃ A 5 G\simeq A_{5} or G ≃ PSU ( 3 , 4 ) G\simeq\mathrm{PSU}(3,4) . This provides an affirmative answer to Problem 19.36 in the Kourovka notebook.
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