Timeline for When is Inn(X) simple?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 22, 2010 at 23:39 | comment | added | Jack Schmidt | Thanks! That makes the situation very clear. In general Z(X)∩X′ need not be a summand of Z(X), but of course it is in the elementary abelian case. | |
| Nov 22, 2010 at 22:18 | comment | added | Derek Holt | In that case (assuming $X$ finite of course) $Z(X)$ is a direct product of elementary abelian groups, so don't we get $Z(X) = (Z(X) \cap X') \times A$ for some $A$ and then $X = X' \times A$? | |
| Nov 22, 2010 at 22:05 | comment | added | Jack Schmidt | If Z(X) has no elements of prime-squared order, must X' be a direct factor? It seemed like H^2(X/Z(X),p) would control it, and that it would not allow anything exciting. Maybe this also just follows by thinking about the definition of central product long enough? | |
| Nov 22, 2010 at 20:57 | history | answered | Derek Holt | CC BY-SA 2.5 |