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Group algebras and algebras of Golod-Shafarevich


Author: Plamen N. Siderov
Journal: Proc. Amer. Math. Soc. 100 (1987), 424-428
MSC: Primary 16A27
MathSciNet review: 891139
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Abstract: In [2], Golod, using results of Golod and Shafarevich [1], has constructed a finitely generated algebra $ A = K\left\langle {{y_1}, \ldots ,{y_d}} \right\rangle $, over any field $ K$, such that the ideal generated by $ {y_1}, \ldots ,{y_d}$ is nil, but $ {\dim _K}A = \infty $. Moreover, when char $ K = p > 0$, the subgroup $ G$ of the group of units of $ A$, generated by $ 1 + {y_1}, \ldots ,1 + {y_d}$, is an infinite $ p$-group. The main purpose of the present paper is to show that $ K[G]$, the group algebra of $ G$ over $ K$, is not isomorphic to $ A$ for "most" Golod-Shafarevich groups $ G$.


References [Enhancements On Off] (What's this?)

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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0891139-9
Article copyright: © Copyright 1987 American Mathematical Society