This article is cited in 5 papers

Groups critical with respect to the spectra of alternating and sporadic groups

Yu. V. Lytkin<sup>ab

a</sup> Novosibirsk State University, Novosibirsk, Russia
^b Siberian State University of Telecommunications and Information Sciences, Novosibirsk, Russia

Abstract: The spectrum of a finite group is the set of its element orders. A finite group $G$ is critical with respect to a subset $\omega$ of natural numbers, if $\omega$ is equal to the spectrum of $G$ and not equal to the spectrum of any proper section of $G$. We give full description of the finite groups critical with respect to the spectrum of the alternating group of degree 10 and the second Janko group.

Keywords: finite group, spectrum, critical group, nonabelian simple group.

UDC: 512.542

Received: 29.09.2014

 English version: Siberian Mathematical Journal, 2015, 56:1, 101–106

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