Nonabelian group of order $p^n$ for every $p$ prime and $n \in \mathbb{N}$  My idea was to just create some sort of generalized dihedral group, that's what I called it at least, maybe it is.  $G = &lt;x,y | x^{p^{n-2}}=1,y^{p^2}=1, y^{-1}xy=x^{-1}&gt;$  Will this work?
Question:      Let $p$ be any prime and $n \geq 3$. Show that there exists a non-abelian group of order $p^n$.    Attempt:   Take $n = 3$. Writing $\mathbb Z_p \times \mathbb Z_p = \{e, \alpha_1, \ldots, \alpha_{p^2 - 1}\}$ and considering $$\begin{align}\tau_{jk} : \mathbb Z_p \times \mathbb Z_p&amp;\to \mathrm {Aut} (\mathbb Z_p)\,\\e &amp;\mapsto id\\\alpha_j &amp;\mapsto id \\\alpha_i &amp;\mapsto \rho_k  \end{align}$$  $\forall i \neq j$ where $\rho_k : \mathbb Z_p \to \mathbb Z_p$ is such that $\rho_k (1) = k$, with $k \in \{2, \ldots, p-1\}$. Then we take the group $(\mathbb Z_p \times \mathbb Z_p) \ltimes_{\tau_{jk}} \mathbb Z_p$.   Then $$(\alpha_i , 2) \ltimes_{\tau_{jk}} (\alpha_i, 1) = (2\alpha_i, 1  + \tau_{jk} (\alpha_i)(2)) = (2\alpha_i , 1  +2 k)$$  and $$(\alpha_i , 1) \ltimes_{\tau_{jk}} (\alpha_i, 2) = (2\alpha_i, 1  + \tau_{jk} (\alpha_i)(2)) = (2\alpha_i , 1  +k)$$  taking $k = 1$ for example we have that the group $(\mathbb Z_p \times \mathbb Z_p) \ltimes_{\tau_{jk}} \mathbb Z_p$ is not abelian.    I was wondering if this is a good aproach. If not, is there an easier way to reach the result?  If this is the "best" way then would the higher cases ($n &gt; 3$) be more of a notation play game?
Error in pip: unsupported operand type(s) for -=: 'Retry' and 'int' I'm trying install the requests, but I can't do that. I'm using Ubuntu 16.04  I tried to install using  $ sudo pip install requests   and I get the following error   Collecting requests Exception: Traceback (most recent call last):   File "/usr/lib/python2.7/dist-packages/pip/basecommand.py", line 209, in main     status = self.run(options, args)   File "/usr/lib/python2.7/dist-packages/pip/commands/install.py", line 317, in run     requirement_set.prepare_files(finder)   File "/usr/lib/python2.7/dist-packages/pip/req/req_set.py", line 360, in prepare_files     ignore_dependencies=self.ignore_dependencies))   File "/usr/lib/python2.7/dist-packages/pip/req/req_set.py", line 512, in _prepare_file     finder, self.upgrade, require_hashes)   File "/usr/lib/python2.7/dist-packages/pip/req/req_install.py", line 273, in populate_link     self.link = finder.find_requirement(self, upgrade)   File "/usr/lib/python2.7/dist-packages/pip/index.py", line 442, in find_requirement     all_candidates = self.find_all_candidates(req.name)   File "/usr/lib/python2.7/dist-packages/pip/index.py", line 400, in find_all_candidates     for page in self._get_pages(url_locations, project_name):   File "/usr/lib/python2.7/dist-packages/pip/index.py", line 545, in _get_pages     page = self._get_page(location)   File "/usr/lib/python2.7/dist-packages/pip/index.py", line 648, in _get_page     return HTMLPage.get_page(link, session=self.session)   File "/usr/lib/python2.7/dist-packages/pip/index.py", line 757, in get_page     "Cache-Control": "max-age=600",   File "/usr/share/python-wheels/requests-2.9.1-py2.py3-none-any.whl/requests/sessions.py", line 480, in get     return self.request('GET', url, **kwargs)   File "/usr/lib/python2.7/dist-packages/pip/download.py", line 378, in request     return super(PipSession, self).request(method, url, *args, **kwargs)   File "/usr/share/python-wheels/requests-2.9.1-py2.py3-none-any.whl/requests/sessions.py", line 468, in request     resp = self.send(prep, **send_kwargs)   File "/usr/share/python-wheels/requests-2.9.1-py2.py3-none-any.whl/requests/sessions.py", line 597, in send     history = [resp for resp in gen] if allow_redirects else []   File "/usr/share/python-wheels/requests-2.9.1-py2.py3-none-any.whl/requests/sessions.py", line 195, in resolve_redirects     **adapter_kwargs   File "/usr/share/python-wheels/requests-2.9.1-py2.py3-none-any.whl/requests/sessions.py", line 576, in send     r = adapter.send(request, **kwargs)   File "/usr/share/python-wheels/CacheControl-0.11.5-py2.py3-none-any.whl/cachecontrol/adapter.py", line 46, in send     resp = super(CacheControlAdapter, self).send(request, **kw)   File "/usr/share/python-wheels/requests-2.9.1-py2.py3-none-any.whl/requests/adapters.py", line 376, in send     timeout=timeout   File "/usr/share/python-wheels/urllib3-1.13.1-py2.py3-none-any.whl/urllib3/connectionpool.py", line 610, in urlopen     _stacktrace=sys.exc_info()[2])   File "/usr/share/python-wheels/urllib3-1.13.1-py2.py3-none-any.whl/urllib3/util/retry.py", line 228, in increment     total -= 1 TypeError: unsupported operand type(s) for -=: 'Retry' and 'int'   My python version is the 2.7 and the pip is 8.1.1 In a PHP5 class, when does a private constructor get called? Let's say I'm writing a PHP (>= 5.0) class that's meant to be a singleton.  All of the docs I've read say to make the class constructor private so the class can't be directly instantiated.  So if I have something like this:  class SillyDB {   private function __construct()   {    }    public static function getConnection()   {    } }   Are there any cases where __construct() is called other than if I'm doing a   new SillyDB()    call inside the class itself?    And why am I allowed to instantiate SillyDB from inside itself at all? Let $\mathbb{F}$ be a finite field.  Let $a_1,\dots,a_n \in \mathbb{F}$ be given.  I want to know whether there exists $x_1,\dots,x_n \in \mathbb{F}$ such that  $$a_1 x_1^2 + a_2 x_2^2 + \dots + a_n x_n^2 = 1.$$  My question: Can we characterize when this equation has a solution, i.e., by some criterion on $a_1,\dots,a_n$?  Is there a clean characterization, in terms of $a_1,\dots,a_n$ and the properties of $\mathbb{F}$?    Here's what I can see immediately.  First, if $n=1$, there is an easy answer (the equation has a solution iff $a_1$ is a square in $\mathbb{F}$).  Second, if any $a_i$ is a square in $\mathbb{F}$, the equation has a solution (set all other $x_j$'s to $0$), so we can assume that all the $a_i$'s are non-squares and that $n \ge 2$.  Third, if $-1$ is a square in $\mathbb{F}$, then the equation has a solution: we can take $x_2 =  \sqrt{-a_1/a_2} \cdot x_1$.  But what about the case where $-1$ is a non-square in $\mathbb{F}$?  Is it always guaranteed to have a solution in this case? Find the condition on $a$ and $b$ so that the two tangents drawn to the parabola $y^2=4ax$ from a point are normals to the parabola $x^2=4by$ Find the condition on $a$ and $b$ so that the two tangents drawn to the parabola $y^2=4ax$ from a point are normals to the parabola $x^2=4by.$  The required condition is $a^2&gt;8b^2$.I dont know how to prove it.I tried.  Let $(h,k)$ be the point from where tangents are drawn to the parabola $y^2=4ax$.Let $m_1,m_2$ be the slopes of the tangents.Equations of tangents are $y=m_1x+\frac{a}{m_1}$ and $y=m_2x+\frac{a}{m_2}$ and equations of normal to the parabola $x^2=4by$ is $y=m_1x-2bm_1-bm^3_1$ and $y=m_2x-2bm_2-bm^3_2$.  As $y=m_1x+\frac{a}{m_1}$ and $y=m_1x-2bm_1-bm^3_1$  are the same lines.Therefore,$\frac{a}{m_1}=-2bm_1-bm^3_1$  $bm^4+2bm^2+a=0$  And I am stuck.I cannot get the desired condition.Please help me. I have a small issue with my Ubuntu (I think After an upgarde). When I try to login (Login Screen), I get disconnected and get back to the screen (again &amp; again).  I tried:   Trying to login with others Desktop environements. Booting from old kernel. log in via command line [apt-get update &amp;&amp; apt-get upgrade]. removing ~/.gconf directory. sudo apt-get install --reinstall ubuntu-desktop and sudo apt-get install unity   None of these solutions worked. How to save picture to iPhone photo library? print python stack trace without exception being raised Environment variables are not passed to sub scripts while running on crontab I was trying to run one of the scripts (for example, wrapper.sh) which internally executes other scripts using crontab. It works fine without any issues.  When I have created a environment file (which stores the passwords-DB and paths) and trying to execute the main script (wrapper.sh) the cron entry doesn't work on those scripts which are called internally in the wrapper.  NOTE: I tried changing PATH, added env file location before the script in cron but it still didn't work:  9 9 * * * . /$SOMEPATH/some.env; /$SOMEPATH/wrapper.sh   The environment script and wrapper.sh are in same path. when the cron runs it passes the env variables to wrapper but not to the scripts which are called internally in wrapper. Also a mail is received on /var/mail/$user saying the env file as "No such file or Directory". I've gone through many posts but couldn't figure out the resolution. Logistic regression vs. LDA as two-class classifiers I have asked this question before ( and  )  My problem is that my Self Encrypted Disk (SED) have to NOT spin down even on suspend!  I have tried , but it did not work and the disk spin downs anyway !  The problem is that if the disk spins down, because it is on suspend, it does not show the "de encryption" prompt, and boots back up on RAM, but crashed due to IO error on the disk! (that's what the disk is suposed to do !)  Anyone on how to NOT (as in NEVER) spin down a HDD ? (yes this goes against all logic but this particular case)   Thanks a lot !  Would that be useful ?   sudo hdparm -I /dev/sda [sudo] password for xqua:   /dev/sda:  ATA device, with non-removable media     Model Number:       ST500LT015-9WU142                            Serial Number:      W0VBZQQ7     Firmware Revision:  0001SDM7     Transport:          Serial, ATA8-AST, SATA 1.0a, SATA II Extensions, SATA Rev 2.5, SATA Rev 2.6 Standards:     Used: unknown (minor revision code 0x0029)      Supported: 8 7 6 5      Likely used: 8 Configuration:     Logical     max current     cylinders   16383   16383     heads       16  16     sectors/track   63  63     --     CHS current addressable sectors:   16514064     LBA    user addressable sectors:  268435455     LBA48  user addressable sectors:  976773168     Logical  Sector size:                   512 bytes     Physical Sector size:                  4096 bytes     Logical Sector-0 offset:                  0 bytes     device size with M = 1024*1024:      476940 MBytes     device size with M = 1000*1000:      500107 MBytes (500 GB)     cache/buffer size  = 16384 KBytes     Form Factor: 2.5 inch     Nominal Media Rotation Rate: 5400 Capabilities:     LBA, IORDY(can be disabled)     Queue depth: 32     Standby timer values: spec'd by Standard, no device specific minimum     R/W multiple sector transfer: Max = 1   Current = 1     Advanced power management level: 254     Recommended acoustic management value: 208, current value: 0     DMA: mdma0 mdma1 mdma2 udma0 udma1 udma2 udma3 udma4 udma5 *udma6           Cycle time: min=120ns recommended=120ns     PIO: pio0 pio1 pio2 pio3 pio4           Cycle time: no flow control=120ns  IORDY flow control=120ns Commands/features:     Enabled Supported:        *    SMART feature set        *    Power Management feature set        *    Write cache        *    Look-ahead        *    Host Protected Area feature set        *    WRITE_BUFFER command        *    READ_BUFFER command        *    NOP cmd        *    DOWNLOAD_MICROCODE        *    Advanced Power Management feature set             Power-Up In Standby feature set        *    SET_FEATURES required to spinup after power up             SET_MAX security extension        *    48-bit Address feature set        *    Device Configuration Overlay feature set        *    Mandatory FLUSH_CACHE        *    FLUSH_CACHE_EXT        *    SMART error logging        *    SMART self-test        *    General Purpose Logging feature set        *    WRITE_{DMA|MULTIPLE}_FUA_EXT        *    64-bit World wide name        *    IDLE_IMMEDIATE with UNLOAD        *    Write-Read-Verify feature set        *    WRITE_UNCORRECTABLE_EXT command        *    {READ,WRITE}_DMA_EXT_GPL commands        *    Segmented DOWNLOAD_MICROCODE        *    Gen1 signaling speed (1.5Gb/s)        *    Gen2 signaling speed (3.0Gb/s)        *    Native Command Queueing (NCQ)        *    Host-initiated interface power management        *    Phy event counters        *    Idle-Unload when NCQ is active             Device-initiated interface power management        *    Software settings preservation        *    SMART Command Transport (SCT) feature set        *    SCT Write Same (AC2)        *    SCT Features Control (AC4)        *    SCT Data Tables (AC5)             unknown 206[12] (vendor specific)        *    reserved 69[4]        *    reserved 69[7] Logical Unit WWN Device Identifier: 5000c5006a036439     NAA     : 5     IEEE OUI    : 000c50     Unique ID   : 06a036439 Checksum: correct Limit $\frac{x^2y}{x^4+y^2}$ is found using polar coordinates but it is not supposed to exist. Help evaluating a gamma function I will be landing at New Delhi airport. The worth of new laptop  (Lenovo Yoga Idea Pad 13) is about $1000 and old one (Macbook Pro) is > 1 lakh INR. I want to leave the new laptop in India. I have a copy of bill with me but not the original bill. I want to know if I have risk of being charged with custom duty. How did the Tesseract come to Earth from Asgard? Term for group of guys attempting to show who is alpha? Similar to pissing contest - but not in an aggressive manner. Just each guy attempting to out talk one another to show they are the leader / in charge.   Sample sentence:     Well, that meeting was more of a X than being productive with Greg trying to show he was in control. I can't delete more than 5 of my own posts in a single day. Is this a bug, or intended behavior? I'm trying to clean up old, crappy posts of mine.    Similar-looking problem, but it claims to be : Shutdown and User button missing in panel Can I register a domain name that contains a company name or trademark? I wonder is it legal to register a domain name that contains a company name. For example cococola.cc (considering that this domain name is available). Can I buy and use any domain names that contain a name of a trademark? I recently reviewed a paper (general applied mathematics context). During the review, I realized that the fairly general ideas introduced in the paper can potentially be applied to a specific problem in a similar context. The authors did not mention this application in their paper, so I suggested to add a short comment about it in my review.  I later started thinking about the application in more detail and tried out some things, which actually seem to work quite well for this application. Now, the paper is still in the review process and might take some time until it gets published. What is the proper way how to proceed here in order to use the ideas and results which I in my exclusive position as a reviewer saw? How can I refer to the paper that is still under review? How can I best discuss the ideas with my co-workers (and potential co-authors) without disclosing that I reviewed the paper?  The paper under review is not available online on any preprint servers such as arXiv etc What is the right way to get the current users profile in an apex class?  When I tried to print the following in visualforce page,  i am able to get the profile name  &lt;apex:outputText value="{!$Profile.Name}"/&gt;    But when i tried to print in the Apex class using System.debug(Profile.Name), I couldn't.