Suppose that $H$ and $K$ are two subgroups of a group $G$.Assume that $[G:H]=2$ and $K$ is not a subgroup of $H$.Show that $HK=G$. Since Index of $H$ in $G$ is $2$ , $H$ is a normal subgroup of $G$ and $K$ is a subgroup of $G$ hence $HK=KH$ is a subgroup of $G$.Now, how to prove  $HK=G$?
i know that|$S_n$|=$n!$ and |$A_n$|= $\frac{n!}{2}$ but i'm not sure where to go from there. Thanks.
How to show wifi password? Let me say first that I am fairly new here (about 3 weeks) and absolutely love Stack Overflow. At first I let some of the negative attitudes get to me a little, left a few snarky comments, but that phase has passed. I see the tremendous value for this site in the long run and sincerely do want to help make it a better place.  I find myself going for  the downvote very frequently -- currently about 35% of my votes are downvotes. I even make an extra effort to upvote good content to offset this a bit, so the number should probably be more like 60%. I always try to leave constructive comments and try to help out the confused ones who are really trying.  I truly can't tell if it is just me, or if these folks deserve it. I don't know if you guys noticed, but there are a lot of really bad questions being posted, and a lot of people trying to pass off things like "use jQuery", "use Firebug", and "use Google" as good answers (and getting upvotes!). I even saw someone copy/paste my "What does Firebug say?" comment as an answer and get 3 votes within moments. Sometimes This answer is unclear or not useful just doesn't do it justice.  I feel like some of the people just drive me nuts, but then again I feel this way IRL :) Am I being too harsh, or is it really that bad on SO? Has there recently been a surge of new users, and the quality of content is degrading, or was it like this in the "good old days"? Have I perhaps misunderstood the expected behavior on Stack Overflow -- should I just ignore these crappy questions and answers rather than downvote them? I am trying to use a  as input and then creating a query with it - so I need a .    I was surprised to find that it couldn't do the conversion implicitly or explicitly - but I don't even know how I would do this, as the Java API is still fairly new to me. Story with VR worlds for the wealthy I realize that I lack any numerical intuition for logarithms. 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