Timeline for non-split extension and Schur multiplier
Current License: CC BY-SA 3.0
2 events
| when toggle format | what | by | license | comment | |
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| Jul 7, 2013 at 9:59 | comment | added | Tina | According to a paper by Dixon and Zalesski(Finite imprimitive linear groups of prime degree, J.Algebra (276)340-370), we have "Suppose that $H$ is a perfect group and consider $Z_p$ as a $ZH$-module with trivial action. Then $H^2(H,Z_p)\neq0$ that is, there exist non-split central extensions of $Z_p$ by $H$ if and only if $p$ divides the order of the Schur multiplier $M(H)$ of $H$." So in my question, if $H$ is a simple group and $K=Z_p$, then my conclusion is right. But, I am interested in the other cases for $Z_p$. Can I replace $Z_p$ with abelian groups or some other groups? | |
| Jul 5, 2013 at 9:48 | history | answered | Alex B. | CC BY-SA 3.0 |