Simple example of an non-cyclic group I'm very familiar with cyclic groups, but I can't seem to understand what a non-cyclic group is like... is there a simple example of one?  (edited... I had no idea that non-cyclic != acyclic)
What are a few examples of noncyclic finite groups? I just want to make sure that every group $\mathbb{Z}_n$ for any $n$ is cyclic. Further, every group of prime order is cyclic because it is isomorphic to $\mathbb{Z}_p$. I think I have a handle on that, but what other finite groups are there that aren't cyclic? In particular, I'm looking for examples that aren't direct products of groups, just simply groups like $\mathbb{Z}_n$, not $\mathbb{Z}_a \times \mathbb{Z}_b$, etc.
Should I be worried that yum update suddenly wants to update well over 100 packages on my CentOS 6 system? How close would you have to be to the merger of two black holes, for the effects of gravitational waves to be detected without instruments? Can an Indian travel to India with 50 days before passport expires? My wife is travelling from Philadelphia to India in January 2019 and, on her outbound trip, she will only have 50 days validity left on her passport. However, while in India, she will be renewing her passport. The reply from a similar question seems to answer point 1 below, but I wanted a second opinion to be sure.  Here are the questions we have:  Can she travel from the US to India via Doha, Qatar with passport validity of only 50 days? Can we make a reservation on Qatar Airways for the roundtrip travel using her current passport and before the return from India to the US update passport information on the reservation? How do I upgrade from 14.04 LTS to 16.04.1 LTS? I am looking for an animated series, shown in the 90s. I remember an episode where the boy went into VR and fought a medusa-like monster.  It may be that this was the premise for the whole series: That the children heroes go into VR every time to fight the evil guys.   I am not sure if the whole series were computer-animated but surely there were such elements together with classic animation.  The style of the series was quite dark and cool for teenage boys. How can I have colored and underlined links with hyperref? Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$ I have to prove that:     $$\sum_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$$   I tried to open up the right side with Pascal's definition that: $$ { n \choose k} = {n-1 \choose {k}} + {n-1 \choose {k-1}}$$  Here is what I came up with, and I am sure it is wrong because it does not equal the left side:  $$ {m+n+1 \choose m+1} = {m+n \choose m+1} + {m+n \choose m} = ... ={m+n \choose m+1} + {m+n-1 \choose m} + {m+n-2 \choose m-1} + ... + {m \choose m+1} = \sum_{k=0}^{n} {m+k \choose m+k-n+1 }  $$  Which, again, probably is wrong because it is not equal $\sum_{k=0}^{n} { m+k \choose m}$. Any help is appreciated Ubuntu in VirtualBox wants to install on every boot I have installed Ubuntu 11.10 using Virtual Box in my Windows XP. I have use Ubuntu 11.10 iso to install it. First time when I installed every thing was fine but when I shutdown the VirtualBox and start Ubuntu again, it asks me to install Ubuntu and try Ubuntu without installing.  Do I need to do some extra settings? I have  a  requirement where a future method need to be called from batch apex ,I came across various articles stating that a future method could not be called from the batch. Is there any alternate solutions for that? Ownership of .Xauthority transferred to root Somehow, while playing around with LightDM and Webkit Greeter, the ownership of the .Xauthority file in my home dir was given to the root user and I couldn't login because I hadn't the privilegues to lock the file.  I was able to regain ownership of the file and I could login again. (After several hours of reinstalling LightDM and it's greeters)  So now everything's working fine again. But I'd like to know how this happened. Is this a bug in LightDM or Webkit Greeter or something else? The definitive guide to ConTeXt MkIV documentation How can we differentiate between change and progress in the area of history and natural sciences? Intellisense in IntelliJ no longer working Ubuntu gets stuck in a login loop My Ubuntu is stuck in a login loop when trying to enter my desktop. When I login, the screen gets black and soon after that the login screen comes back.   I've read that the problem might be caused by an error depending on the graphics, here's my graphics card: ATI Radeon 7670M Report this Ad Feature Why does the experience-to-next-level not change between some levels? At every level from 1st to 11th, the experience needed to reach the next level (from the current level) increases every level. However, this pattern gets broken for most of the later levels:   Going from 10th to 11th takes 21,000xp (= 85k - 64k), but 11th to 12th takes only 15,000xp! (= 100k - 85k). Both 13th and 14th level only take extra 20k experience each, i.e. the amount needed doesn't increase between those two levels. Levels 16 and 17 similarly only need 30k experience each, and 18 and 19 only need 40k experience each.   Why does the last half of the experience chart have some of these levels maintain the same experience costs, and even briefly decrease the experience cost for 12th level? The link here:  shows that $\max(a,b)=\frac{a+b+|a-b|}{2}$.      Is it true that $\max(|a|,|b|)=\frac{1}{2}(|a|+|b|)$? Changing planes at Newark Airport I fly in from Sweden with United to Newark Liberty Airport. The connecting flight with United departs to Costa Rica a few hours later from Newark as well. The two flight-segments are part of the same trip and ticket.  I was hoping to stay in the same terminal but am suspecting that it wont be as straightforward as I had hoped - reading through the older posts it seems that a transfer is needed from A to C but it's not fully clear.   Do I need to pass through immigration? Do I need to fetch our bags? Even if my bags have tags all the way to SJO? Do I need to change terminals? Which terminal would I arrive in? Depart from? Is it possible to have a 100% secure virtual private server? I am curious if it is possible to have a VPS that has data on it that is not readable by the hosting provider, but is still usable on the VPS.  Obviously there are some things that you could do to prevent them from reading anything...   You could change all the passwords, including root. But then, they could still use some alternate boot to reset the password, or they could just mount the disk another way. So, you could encrypt the disk or at least some of the contents on the disk. But then it seems that if you decrypted the content, they could still "peer in" to see what you were doing at the console, because after all, the virtualization platform should allow this. And even if you could stop that, it seems they could just read the RAM of the VPS directly.   Of course, the VPS can store data on it and as long as the key is not on the VPS and the data is never decrypted there, then the host cannot get the data.  But it seems to me that if any point the data on the VPS is decrypted...for use on the VPS...then the hosting provider can get the data.  So, my two questions are:   Is this correct? Is it true that there is no way to 100% secure data on a VPS from a host from seeing it, while keeping it accessable by the VPS? If it is possible to make it 100% secure, then how? If it is not possible, then what is the closest you can get to hiding data from the web host? Should I defragment my SSD?