Consider the following situation: I have given a finite $p$-group $P$ (in the case I am interested in $p = 2$) with cyclic center $Z(P)$ and I also know the structure of the quotient $P/Z(P)$ (which is non-trivial). What are the possible isomorphism types of $P$? Of course, in general a central extension such as $P$ is not unique. However, I wonder whether in this particular situation more can be said about the structure of $P$. For example, $P$ cannot be the trivial extension, because otherwise the center would be too large.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.