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

Khatri, D. C.

doi:10.1090/S0002-9947-1973-0327880-0

Relative projectivity, the radical and complete reducibility in modular group algebras
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by D. C. Khatri PDF

Trans. Amer. Math. Soc. 186 (1973), 51-63 Request permission

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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