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This article is cited in 2 scientific papers (total in 2 papers)
Finite-dimensional algebras of integral $p$-adic representations of finite groups
P. M. Gudivok, S. F. Goncharova, V. P. Rud'ko
Abstract:
Let $F$ be a inite extension of the field of rational $p$-adic numbers $Q_p$, $R$ he ring of integers of $F$, $G$ a finite group, $a(RG)$ the ring of $R$-representations of $G$ and $A(RG)=Q\otimes_Za(RG)$ ($Z$ is the ring of rational integers and $Q$ the rational number field). We study the algebra $A(RG)$ in the case where the number $n(RG)$ of indecomposable $R$-representations of $G$ is finite. In particular, for $G$ a $p$-group and $n(RG)<\infty$ we find a list of the tensor products of indecomposable $R$-representations of $G$ and obtain a description of the radical $N$ of $A(RG)$ and of the quotient algebra $A(RG)/N$. It turns out that in this case we always have $N^2=0$.
Bibliography: 26 titles.
Received: 07.03.1973
Citation:
P. M. Gudivok, S. F. Goncharova, V. P. Rud'ko, “Finite-dimensional algebras of integral $p$-adic representations of finite groups”, Mat. Sb. (N.S.), 94(136):3(7) (1974), 358–384; Math. USSR-Sb., 23:3 (1974), 336–361
Linking options:
https://www.mathnet.ru/eng/sm3687https://doi.org/10.1070/SM1974v023n03ABEH001721 https://www.mathnet.ru/eng/sm/v136/i3/p358
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Abstract page: | 275 | Russian version PDF: | 92 | English version PDF: | 9 | References: | 35 |
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