Abstract
It is proven that if K is a commutative ring of characteristic pm while group G contains p-elements, then the multiplicative group UKG of group ring KG is nilpotent if and only if G is nilpotent and its commutant G′ is a finite p-group. Those group algebras KG are described for which the nilpotency classes of groups G and UKG coincide.
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Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 191–200, February, 1972.
In conclusion, the author wishes to express her gratitude to A. A. Bovdi for his scientific direction.
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Khripta, I.I. Nilpotency of the multiplicative group of a group ring. Mathematical Notes of the Academy of Sciences of the USSR 11, 119–124 (1972). https://doi.org/10.1007/BF01097929
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DOI: https://doi.org/10.1007/BF01097929