Geodesic
On the Prime Radical of $PI$-Representable Groups
Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 739-744

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The notion of $PI$-representable groups is introduced; these are subgroups of invertible elements of a $PI$-algebra over a field. It is shown that a $PI$-representable group has a largest locally solvable normal subgroup, and this subgroup coincides with the prime radical of the group. The prime radical of a finitely generated $PI$-representable group is solvable. The class of $PI$-representable groups is a generalization of the class of linear groups because in the groups of the former class the largest locally solvable normal subgroup can be not solvable. 
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     author = {S. A. Pikhtilkov},
     title = {On the {Prime} {Radical} of $PI${-Representable} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {739--744},
     publisher = {mathdoc},
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     number = {5},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_5_a12/}
}
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S. A. Pikhtilkov. On the Prime Radical of $PI$-Representable Groups. Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 739-744. http://geodesic.mathdoc.fr/item/MZM_2002_72_5_a12/