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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Group algebras whose simple modules are injective


Authors: Daniel R. Farkas and Robert L. Snider
Journal: Trans. Amer. Math. Soc. 194 (1974), 241-248
MSC: Primary 16A26
MathSciNet review: 0357475
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Abstract: Let F be either a field of char 0 with all roots of unity or a field of char $ p > 0$. Let G be a countable group. Then all simple $ F[G]$-modules are injective if and only if G is locally finite with no elements of order char F and G has an abelian subgroup of finite index.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0357475-5
PII: S 0002-9947(1974)0357475-5
Keywords: Injective simple module, group algebra, locally finite groups
Article copyright: © Copyright 1974 American Mathematical Society



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