2009•Proceedings of the Steklov Institute of MathematicsRequires access
On recognizability of some finite simple orthogonal groups by spectrum
O. A. Alekseeva, А. С. Кондратьев
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Abstract
It is proved that, if G is a finite group that has the same set of element orders as the simple group D p (q), where p is prime, p ≥ 5 and q ∈ {2, 3, 5}, then the commutator group of G/F(G) is isomorphic to D p (q), the subgroup F(G) is equal to 1 for q = 5 and to O q (G) for q ∈ {2, 3}, F(G) ≤ G′, and |G/G′| ≤ 2.