Compute all $X_{g}$ and all $G_{x}$ for $X = left {1, 2, 3right }$, $G = S_{3} = left {(1), (12), (13), (23),...












1












$begingroup$



Compute all $X_{g}$ and all $G_{x}$ for $X = left {1, 2, 3right }$, $G = S_{3} = left {(1), (12), (13), (23), (123), (132)right }$.




Can someone give me a head start to this problem?



$X_{g}=left {xin X: gx=xright }$. So how do I find $X_{(12)}$? Do I calculate $(12)(1),(12)(2),(12)(3)$?






abstract-algebra group-theory permutations group-actions permutation-cycles







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Yes. But then, you see, $(12)$ is the permutation that affects only $1$ and $2$, so it doesn't affect any other number. So $X_{(12)}$ should be immediate.
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:01










  • $begingroup$
    And so $X_{(12)}=left {3right }$?
    $endgroup$
    – numericalorange
    Dec 5 '18 at 19:17








  • 1




    $begingroup$
    That's absolutely right!
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:30










  • $begingroup$
    @Scientifica Oh, wow, I feel so happy that you helped me understand this so easily!!
    $endgroup$
    – numericalorange
    Dec 5 '18 at 19:31






  • 1




    $begingroup$
    I'm gonna post this as an answer so that your question is answered.
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:32
















1












$begingroup$



Compute all $X_{g}$ and all $G_{x}$ for $X = left {1, 2, 3right }$, $G = S_{3} = left {(1), (12), (13), (23), (123), (132)right }$.




Can someone give me a head start to this problem?



$X_{g}=left {xin X: gx=xright }$. So how do I find $X_{(12)}$? Do I calculate $(12)(1),(12)(2),(12)(3)$?






abstract-algebra group-theory permutations group-actions permutation-cycles







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Yes. But then, you see, $(12)$ is the permutation that affects only $1$ and $2$, so it doesn't affect any other number. So $X_{(12)}$ should be immediate.
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:01










  • $begingroup$
    And so $X_{(12)}=left {3right }$?
    $endgroup$
    – numericalorange
    Dec 5 '18 at 19:17








  • 1




    $begingroup$
    That's absolutely right!
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:30










  • $begingroup$
    @Scientifica Oh, wow, I feel so happy that you helped me understand this so easily!!
    $endgroup$
    – numericalorange
    Dec 5 '18 at 19:31






  • 1




    $begingroup$
    I'm gonna post this as an answer so that your question is answered.
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:32














1












1








1


1



$begingroup$



Compute all $X_{g}$ and all $G_{x}$ for $X = left {1, 2, 3right }$, $G = S_{3} = left {(1), (12), (13), (23), (123), (132)right }$.




Can someone give me a head start to this problem?



$X_{g}=left {xin X: gx=xright }$. So how do I find $X_{(12)}$? Do I calculate $(12)(1),(12)(2),(12)(3)$?






abstract-algebra group-theory permutations group-actions permutation-cycles







share|cite|improve this question











$endgroup$





Compute all $X_{g}$ and all $G_{x}$ for $X = left {1, 2, 3right }$, $G = S_{3} = left {(1), (12), (13), (23), (123), (132)right }$.




Can someone give me a head start to this problem?



$X_{g}=left {xin X: gx=xright }$. So how do I find $X_{(12)}$? Do I calculate $(12)(1),(12)(2),(12)(3)$?






abstract-algebra group-theory permutations group-actions permutation-cycles




abstract-algebra group-theory permutations group-actions permutation-cycles






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 5 '18 at 19:34









Scientifica

6,79641335




6,79641335










asked Dec 5 '18 at 18:56









numericalorangenumericalorange

1,775311




1,775311








  • 1




    $begingroup$
    Yes. But then, you see, $(12)$ is the permutation that affects only $1$ and $2$, so it doesn't affect any other number. So $X_{(12)}$ should be immediate.
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:01










  • $begingroup$
    And so $X_{(12)}=left {3right }$?
    $endgroup$
    – numericalorange
    Dec 5 '18 at 19:17








  • 1




    $begingroup$
    That's absolutely right!
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:30










  • $begingroup$
    @Scientifica Oh, wow, I feel so happy that you helped me understand this so easily!!
    $endgroup$
    – numericalorange
    Dec 5 '18 at 19:31






  • 1




    $begingroup$
    I'm gonna post this as an answer so that your question is answered.
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:32














  • 1




    $begingroup$
    Yes. But then, you see, $(12)$ is the permutation that affects only $1$ and $2$, so it doesn't affect any other number. So $X_{(12)}$ should be immediate.
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:01










  • $begingroup$
    And so $X_{(12)}=left {3right }$?
    $endgroup$
    – numericalorange
    Dec 5 '18 at 19:17








  • 1




    $begingroup$
    That's absolutely right!
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:30










  • $begingroup$
    @Scientifica Oh, wow, I feel so happy that you helped me understand this so easily!!
    $endgroup$
    – numericalorange
    Dec 5 '18 at 19:31






  • 1




    $begingroup$
    I'm gonna post this as an answer so that your question is answered.
    $endgroup$
    – Scientifica
    Dec 5 '18 at 19:32








1




1




$begingroup$
Yes. But then, you see, $(12)$ is the permutation that affects only $1$ and $2$, so it doesn't affect any other number. So $X_{(12)}$ should be immediate.
$endgroup$
– Scientifica
Dec 5 '18 at 19:01




$begingroup$
Yes. But then, you see, $(12)$ is the permutation that affects only $1$ and $2$, so it doesn't affect any other number. So $X_{(12)}$ should be immediate.
$endgroup$
– Scientifica
Dec 5 '18 at 19:01












$begingroup$
And so $X_{(12)}=left {3right }$?
$endgroup$
– numericalorange
Dec 5 '18 at 19:17






$begingroup$
And so $X_{(12)}=left {3right }$?
$endgroup$
– numericalorange
Dec 5 '18 at 19:17






1




1




$begingroup$
That's absolutely right!
$endgroup$
– Scientifica
Dec 5 '18 at 19:30




$begingroup$
That's absolutely right!
$endgroup$
– Scientifica
Dec 5 '18 at 19:30












$begingroup$
@Scientifica Oh, wow, I feel so happy that you helped me understand this so easily!!
$endgroup$
– numericalorange
Dec 5 '18 at 19:31




$begingroup$
@Scientifica Oh, wow, I feel so happy that you helped me understand this so easily!!
$endgroup$
– numericalorange
Dec 5 '18 at 19:31




1




1




$begingroup$
I'm gonna post this as an answer so that your question is answered.
$endgroup$
– Scientifica
Dec 5 '18 at 19:32




$begingroup$
I'm gonna post this as an answer so that your question is answered.
$endgroup$
– Scientifica
Dec 5 '18 at 19:32










1 Answer
1






active

oldest

votes


















1












$begingroup$

Yes that's how you do it.



You can also easily see it as follows: the permutation $(12)$ affects $1$ and $2$, but no other element. So $X_{(12)}$ is immediate. The same remark allows you to quickly determine the $G_x$.






share|cite|improve this answer









$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "69"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: true,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: 10,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027493%2fcompute-all-x-g-and-all-g-x-for-x-left-1-2-3-right-g-s%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1












    $begingroup$

    Yes that's how you do it.



    You can also easily see it as follows: the permutation $(12)$ affects $1$ and $2$, but no other element. So $X_{(12)}$ is immediate. The same remark allows you to quickly determine the $G_x$.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      Yes that's how you do it.



      You can also easily see it as follows: the permutation $(12)$ affects $1$ and $2$, but no other element. So $X_{(12)}$ is immediate. The same remark allows you to quickly determine the $G_x$.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        Yes that's how you do it.



        You can also easily see it as follows: the permutation $(12)$ affects $1$ and $2$, but no other element. So $X_{(12)}$ is immediate. The same remark allows you to quickly determine the $G_x$.






        share|cite|improve this answer









        $endgroup$



        Yes that's how you do it.



        You can also easily see it as follows: the permutation $(12)$ affects $1$ and $2$, but no other element. So $X_{(12)}$ is immediate. The same remark allows you to quickly determine the $G_x$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 5 '18 at 19:34









        ScientificaScientifica

        6,79641335




        6,79641335






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematics Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027493%2fcompute-all-x-g-and-all-g-x-for-x-left-1-2-3-right-g-s%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            How to send String Array data to Server using php in android

            Image
            0 I have a String array which contains value string array = {6,37,38,837,7,...} and I have also used some string values. I want to send that all string values and string array to my database which is located at server side. When I am click on submit button the data will stored in table. On the PHP side I want to read this array as it is,other thing i will do at background means PHP side. See my below code then you will get it what I am says. Here is my code: public class Hotels extends Activity { // Declare Variables JSONArray jsonarray = null; private static final String TAG_ID = "id"; public static final String TAG_NAME = "name"; public static final String TAG_LOCATION = "location"; public static final String TAG_DESC = "description"; String f_date, l_date;...
            Read more

            Title Spacing in Bjornstrup Chapter, Removing Chapter Number From Contents

            Image
            up vote 5 down vote favorite 2 I would like to make it so that the vertical space below the title of each chapter is the same when using the Bjornstrup package (i.e. so that the descenders do not affect the spacing - as shown by the red arrow in the picture below). I think I'm fairly happy with the spacing around "A chapter", so I'd really like titles without descenders (e.g. "Contents") to have the same vertical spacing as "A chapter" below the title. I would also like to remove the large "0" in the contents title. Any help appreciated, as always. documentclass[11pt,a4paper]{book} % Packages[![enter image description here][1]][1] usepackage[left=3.5cm, right=3.5cm, top=4.3cm, bottom=4.25cm]{geometry} usepackage[utf8]{inputenc} usepackage{libertine} usepackage[libertine]{newtx...
            Read more

            Is anime1.com a legal site for watching anime?

            Image
            up vote 4 down vote favorite 1 Other anime streaming sites are blocking my IP because I'm Iranian while anime1.com isn't. I wanted to know if it's legal to watch/stream anime from this site. Thanks. anime-production share | improve this question edited Nov 27 at 22:38 W. Are 1,599 2 23 asked Nov 27 at 20:36 mhnajafi 23 3 add a comment ...
            Read more