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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Relative projectivity, the radical and complete reducibility in modular group algebras

Author: D. C. Khatri
Journal: Trans. Amer. Math. Soc. 186 (1973), 51-63
MSC: Primary 20C05
MathSciNet review: 0327880
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Abstract: If $H \leq G$ and every G-module is H-projective then (G, H) is a projective pairing. If Rad $FG \subseteq ({\text {Rad}}\;FH)FG$ then (G, H) is said to have property p. A third property considered is that for each irreducible H-module the induced G-module be completely reducible. It is shown that these three are equivalent properties in many interesting cases. Also examples are given to show that they are, in general, independent of each other.

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Keywords: Projective pairing, Jacabson radical, complete reducibility, Frobenius groups
Article copyright: © Copyright 1973 American Mathematical Society