Recognizing by Spectrum for the Automorphism Groups of Sporadic Simple Groups
V. D. Mazurov , A. R. Moghaddamfar
Communications in Mathematics and Statistics ›› 2015, Vol. 3 ›› Issue (4) : 491 -496.
Recognizing by Spectrum for the Automorphism Groups of Sporadic Simple Groups
The spectrum of a finite group is the set of its element orders, and two groups are said to be isospectral if they have the same spectra. A finite group G is said to be recognizable by spectrum, if every finite group isospectral with G is isomorphic to G. We prove that if S is one of the sporadic simple groups $M^cL$, $M_{12}$, $M_{22}$, He, Suz and $O'N$, then $\mathrm{Aut}(S)$ is recognizable by spectrum. This finishes the proof of the recognizability by spectrum of the automorphism groups of all sporadic simple groups, except $J_2$.
Automorphism groups of sporadic simple groups / Prime graph / Recognizable by spectrum
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