Timeline for Reference for projective covers of direct products of finite groups?
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4, 2011 at 20:33 | comment | added | Geoff Robinson | Well, I think of a Brauer character as defined only on $p$-regular elements, and the "inner product" of Brauer characters as restricted to $p$-regular elements. With this convention, the Brauer characters of the PIMs are uniquely determined once the Brauer characters of the simple modules are. | |
| Nov 29, 2011 at 15:24 | comment | added | Jim Humphreys |
Fein's paper (which has open access) is mainly concerned with working over general fields, adapting Schur index ideas, etc. The case of a splitting field seems fairly straightforward in his module language, but I couldn't find a textbook reference. Use of Brauer characters looks reasonable, though for uniqueness you have to specify that $\theta_i$ is the Brauer character of a projective module. The method I sketched based on dimension comparisons would be fairly direct too if filled in.
|
|
| Nov 29, 2011 at 13:03 | history | answered | Geoff Robinson | CC BY-SA 3.0 |