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 and every *G*-module is *H*-projective then (*G, H*) is a projective pairing. If Rad 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0327880-0

Keywords:
Projective pairing,
Jacabson radical,
complete reducibility,
Frobenius groups

Article copyright:
© Copyright 1973
American Mathematical Society