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 iso...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^(c)L,M_(12),M_(22),He,Suz and O'N,then 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).展开更多
基金This work is supported by Russian Science Foundation(Project No.14-21-00065).
文摘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^(c)L,M_(12),M_(22),He,Suz and O'N,then 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).
