Geodesic
Recognition of Simple Groups $U_3(Q)$ by Element Orders
Algebra i logika, Tome 45 (2006) no. 2, pp. 185-202

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An exhaustive solution is given to the recognition-by-spectrum problem for finite, simple, three-dimensional unitary groups. For every such group, the number of non-isomorphic, finite, isospectral groups is determined. In particular, a new counterexample to Problem 13.63 in the Kourovka Notebook is furnished.
Keywords: finite group, element order, recognition, spectrum. 
@article{AL_2006_45_2_a2,
     author = {A. V. Zavarnitsin},
     title = {Recognition of {Simple} {Groups} $U_3(Q)$ by {Element} {Orders}},
     journal = {Algebra i logika},
     pages = {185--202},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2006_45_2_a2/}
}
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A. V. Zavarnitsin. Recognition of Simple Groups $U_3(Q)$ by Element Orders. Algebra i logika, Tome 45 (2006) no. 2, pp. 185-202. http://geodesic.mathdoc.fr/item/AL_2006_45_2_a2/