A New Characterization of Projective Special Unitary Groups PSU3(3n)

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One of an important problems in finite groups theory, is characterization of groups by specific property. However, in the way the researchers, proved that some of groups by properties such as, elements order, set of elements with same order, graphs, . . . , are characterizable. One of the other methods, is group characterization by using the order of group and the largest elements order. In this paper, we prove that projective special unitary groups PSU3(3n), where 32n−3n+1 is a prime number, can be uniquely determined by the order of group and the second largest elements order.

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