On finite groups isospectral to simple symplectic and orthogonal groups
Copyright policy )On finite groups isospectral to simple symplectic and orthogonal groups
Summary: The spectrum of a finite group is the set of its element orders. Two groups are said to be isospectral if their spectra coincide. We deal with the class of finite groups isospectral to simple and orthogonal groups over a field of arbitrary positive characteristic \(p\). It is known that a group of this class has a unique nonabelian composition factor. We prove that this factor cannot be isomorphic to an alternating or sporadic group. We also consider the case where this factor is isomorphic to a group of Lie type over a field of the same characteristic \(p\).
- Sobolev Institute of Mathematics Russian Federation
spectra of groups, simple groups, composition factors, finite groups, sets of element orders, Linear algebraic groups over finite fields, orthogonal groups, Simple groups: alternating groups and groups of Lie type, symplectic groups, Arithmetic and combinatorial problems involving abstract finite groups, groups of Lie type
spectra of groups, simple groups, composition factors, finite groups, sets of element orders, Linear algebraic groups over finite fields, orthogonal groups, Simple groups: alternating groups and groups of Lie type, symplectic groups, Arithmetic and combinatorial problems involving abstract finite groups, groups of Lie type
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