Geodesic
On the spectrum of sums of generators in a finite group
Izvestiya. Mathematics , Tome 37 (1991) no. 2, pp. 461-463

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Let $K$ be any finite extension field of the field of rationals, and let $n$ and $\alpha_1,\dots,\alpha_n$ be given natural numbers. It is shown that there are only finitely many isomorphism classes of finite groups $G$ on $n$ generators $a_1,\dots,a_n$ such that the spectrum of the element $\sum\limits_{i=1}^n\alpha_ia_i$ of the algebra $\mathbf CG$ lies in $K$. 
@article{IM2_1991_37_2_a9,
     author = {S. P. Strunkov},
     title = {On the spectrum of sums of generators in a finite group},
     journal = {Izvestiya. Mathematics },
     pages = {461--463},
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     volume = {37},
     number = {2},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_37_2_a9/}
}
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S. P. Strunkov. On the spectrum of sums of generators in a finite group. Izvestiya. Mathematics , Tome 37 (1991) no. 2, pp. 461-463. http://geodesic.mathdoc.fr/item/IM2_1991_37_2_a9/