Prime radicals of Chevalley groups over commutative rings (Q5953279)

This is one of a series of papers whose aim is to compute the prime and soluble radicals of Chevalley groups over arbitrary commutative rings \(R\) with unity (for the case \(A_1\), the restriction that 2 and 3 are invertible in \(R\) is needed). The author proves that the prime radical of a Chevalley group over \(R\) is equal to the center of the Chevalley group by the prime radical of \(R\). As a consequence, the existence of the soluble radical in a Chevalley group is equivalent to the nilpotence of the prime radical.