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 Nov 24 comment If $\lim\limits _{x\to\infty}\left(\log f\right)'\left(x\right)$ is negative, then $\int_{0}^{\infty}f\left(x\right)dx$ converges? @Did I didn't really understand your second comment though, but I did take the first one somewhere, and I'd love to know if my answer is correct :P Nov 24 comment If $\lim\limits _{x\to\infty}\left(\log f\right)'\left(x\right)$ is negative, then $\int_{0}^{\infty}f\left(x\right)dx$ converges? @Did Thinking about it so far, still not sure.. Definitely feels like I'm missing something simple though.. Nov 19 comment Powers of linear transformation and minimal polynomial @MarcvanLeeuwen well, I give my reasoning in the question. Setting $T^4$ in the minimal polynomial of $T$ gives you zero, so the minimal polynomial of $T^4$ must divide it... Nov 19 comment Powers of linear transformation and minimal polynomial Well took me a while, but I understand everything. Thank you Nov 19 comment Powers of linear transformation and minimal polynomial Also, I'm not quite sure about the relation $T^14=T^13$. This is obviously true if you look only on the generalized eigenspace of $0$, but what makes it hold true for all of $V$? Nov 19 comment Powers of linear transformation and minimal polynomial Unfortunately I did not understand the answer. How from $(T^4)^5-(T^4)^4=0$ did you get to the minimal polynomial? Nov 10 comment Union of conjugates of a subgroup of a finitely generated group. @Derek Holt Oh I see. That's interesting. Though guess I'll need to come back to it aftrr I've studied the subject for a bit longer.. Nov 6 comment If \$H<. Thank you