Let $G$ be a group  and $\{H_i\}_{i\in \mathcal{I}}$ for some (not necessarily countable) indexing set $\mathcal{I}$ be a family of subgroups of $G$ none of which contain all the others. State and prove a general condition that will imply $\bigcup \limits_{i\in\mathcal{I}}H_i$ is a subgroup of $G$.   After thinking for a day two I ran into the following idea: What if I put the following condition: For any pairs $i,j\in \mathcal{I}$ there is $k\in \mathcal{I}$ such that $H_i\subset H_k$ and $H_j\subset H_k$. And it's quite easy to show that in this case the union of $\{H_i\}_{i\in \mathcal{I}}$ is a subgroup!  But I don't know what to do with the condition "none of which contain all the others"?
Let $G$ be a group and $\{H_i\}_{i\in I}$ a family of subgroups. I would like to find a condition that will imply that $\cup_{i\in I} H_i$ is a subgroup. I know that it's not true in general, I need help to find this condition.  Any help is welcome.  Thanks a lot.
How to stop Time Warner cable search on Firefox for Android? I went into about:config and have the following:  browser.search.defaultenginename Google  browser.search.official true  browser.search.order.1 Google  keyword.URL https://www.google.com/search?p=   And still, when I type in the search bar, it pulls up Time Warner Cable Road Runner search instead of Google. It looks like only if I have more than 1 word does it decide to use google -- maybe using only 1 word means I type a malformed URL? How can I fix this to use Google as a proper search engine? Exclude folder using `find` command I'm using the find command on a Mac to search for a folder called test1. Now test1 folder could be present in the .Trash folder also. 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I don't know is it relevant or not, but I have a lot of free storage space available.  What caused this change? What can I do to prevent this? Like the title says, can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?  I have a feeling the answer is yes because the characteristic polynomial can have coefficients in $\mathbb{C}$ and so I don't see any reason why not, I was merely asking in case there was some sneaky proof that proves that this cannot happen. I have 8 individual SQL Server 2008 R2 machines, each hosting 1 database. Each database has an identical table structure and schema, and entirely unique data.  I would like to establish a reporting server (may be 2008 or 2012), that consolidates the rows  from selected tables across the 8 source servers into a single instance of those tables on the reporting server. This is one-way replication (no changes will be made to the reporting server). 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Do you keep gaining spell slots like a level 20+ character, or does something else happen? In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory take non-zero vacuum expectation value? What forbids fermions to take vevs? What medium should be used for long term, high volume, data storage (archival)? How can I create a custom terminal command (to run a script)? Long rectangular quads? Or neat squarish quads with tris? For curved meshes I've often noticed that in my desperation to avoid tris, I tend to extrude the mesh in a way which creates these long rectangular quads:    In this case at least, the mesh is all quads, however the edge flow causes loopcutting to be awkward in some places:    I tried creating the same mesh with more even topology, however I found tris unavoidable. Maybe it was because I was starting with the long-quad mesh, but I also found myself using the knife tool for everything..    This makes loopcuts less necessary and easier to place in most cases, though the occasional tri does get in the way.  An annoying thing about the tris are the poles, though they aren't too noticeable in this particular case.    Both techniques seems to have their advantages and their disadvantages:    Which is considered "better", if any? Are there any better workflows for creating even topology with as few tris as possible? Or is there some trick I'm missing altogether? I have two tables A &amp; B. Table A id | name | num  Table B id | date | roll  id in table B is a foreign key which relates to the id in table A. I want to get the contents of table B where id is given and also along with that data, I need the name whose id is given from table A. NOTE: cannot use multiple queries separated by commas; need to do both the SELECTs in one query. Installing Nvidia drivers on Red Hat I have this string  'john smith~123 Street~Apt 4~New York~NY~12345'   Using JavaScript, what is the fastest way to parse this into  var name = "john smith"; var street= "123 Street"; //etc... Product of two random variables that has exponential distribution Salesforce lightning get current users username How I would go about getting the current users username or first and last name?  I have been looking at this for the last couple of hours - I was just wondering how I would go about getting their name and then displaying it on the page.  For example the current user is 'John Smith' and in the lightning component I want to output John Smith's name like:     Welcome to our community John Smith! What are watched tags and ignored tags? How do they work? What are tag subscriptions? What are interesting tags? On Stack Overflow, the content of the main page question list appears to be influenced by watched and ignored tags. How does that work?   For more information, see &quot;&quot; in the . Set Theory: Tree Property Why does the tree property hold for regular cardinals but not singular cardinals? (I.e. There exists a tree of height $\kappa$ with countable levels and no cofinal branch for $\kappa$ a singular cardinal)