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Groups isospectral to the degree 10 alternating group


The spectrum of a finite group is the set of its element orders. We describe the composition structure of every finite group with the same spectrum as that of the alternating group of degree 10 and not isomorphic to it. This group is isomorphic to the semidirect product of the abelian {3, 7}-group, which contains an element of order 21, by the symmetric group of degree 5.

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Author information

Correspondence to A. M. Staroletov.

Additional information

Original Russian Text Copyright © 2010 Staroletov A. M.

The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-344.2008.1), the Russian Federal Agency for Education (Grant, and the Lavrent’ev Young Scientists Competition of the Russian Academy of Sciences (Resolution No. 43 of 04.02.2010).


Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 638–648, May–June, 2010.

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Staroletov, A.M. Groups isospectral to the degree 10 alternating group. Sib Math J 51, 507–514 (2010).

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  • spectrum of a group
  • isospectral groups
  • recognition of groups by spectrum
  • simple group
  • Frobenius group
  • alternating group