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Dedicated to 70-th anniversary of V. D. Mazurov Review: The spectrum of a group is the set of its element orders. A finite group G is said to be recognizable by spectrum if every finite group that has the same spectrum as G is isomorphic to G. We prove that the simple alternating groups A n are recognizable by spectrum when n = 6, 10. This implies that every finite group with the same spectrum as that of a finite nonabelian simple group, has at most one nonabelian composition factor.

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Recognizability of Symmetric Groups by Spectrum

Gorshkov

2015

Algebra Logic

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Cited by 31 publications

References 4 publications

OD-characterization of almost simple groups related to U 3(5)

OD-characterization of almost simple groups related to U 3(5)

Recognizability of Alternating Groups by Spectrum

Recognizability of Symmetric Groups by Spectrum

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