Sib. Èlektron. Mat. Izv., 2010, Volume 7, Pages 14–20
This article is cited in 2 scientific papers (total in 2 papers)
Recognition by spectrum for finite simple groups with orders having prime divisors at most 17
I. B. Gorshkov
Novosibirsk State University
The spectrum $\omega(G)$ of a group $G$ is the set of its element orders. We write $h(G)$ to denote the number of pairwise non-isomorphic finite groups $H$ with $\omega(H)=\omega(G)$. We say that $G$ is recognizable by spectrum if $h(G)=1$ and that $G$ is a group with solved recognition-by-spectrum problem if $h(G)$ is known. In the paper we prove that the groups $C_3(4)$ and $D_4(4)$ are recognizable by
spectrum. It follows from this result that the recognition-by-spectrum problem is solved for all finite simple
groups with orders having prime divisors at most $17$.
finite group, simple group, spectrum of a group, recognition by spectrum.
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Received October 28, 2009, published January 21, 2010
I. B. Gorshkov, “Recognition by spectrum for finite simple groups with orders having prime divisors at most 17”, Sib. Èlektron. Mat. Izv., 7 (2010), 14–20
Citation in format AMSBIB
\paper Recognition by spectrum for finite simple groups with orders having prime divisors at most 17
\jour Sib. \`Elektron. Mat. Izv.
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This publication is cited in the following articles:
A. M. Staroletov, “On recognition by spectrum of the simple groups $B_3(q)$, $C_3(q)$, and $D_4(q)$”, Siberian Math. J., 53:3 (2012), 532–538
M. S. Nirova, “Reberno simmetrichnye grafy s chislom vershin, ne bolshim 100”, Sib. elektron. matem. izv., 10 (2013), 22–30
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