A proof of a conjecture by Jabara on groups in which all involutions are odd transpositions

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.