Let k be an integer such that k divides n. Show that H = is a normal subgroup of Dn (Dihedral group). Then,...
Let k be an integer such that k divides n. Show that H = is a normal subgroup of Dn (Dihedral group). Then, show that Dn/H is isomorphic to Dk.
I am totally lost here. I know in Dihedral group, r^n=e=s^2, srs=r^-1. However, I don't know how to proceed this question.
abstract-algebra
asked Nov 19 '18 at 4:50
RandomThinker
192
add a comment |
Let k be an integer such that k divides n. Show that H = is a normal subgroup of Dn (Dihedral group). Then, show that Dn/H is isomorphic to Dk.
I am totally lost here. I know in Dihedral group, r^n=e=s^2, srs=r^-1. However, I don't know how to proceed this question.
abstract-algebra
asked Nov 19 '18 at 4:50
RandomThinker
192
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 '18 at 5:23
add a comment |
Let k be an integer such that k divides n. Show that H = is a normal subgroup of Dn (Dihedral group). Then, show that Dn/H is isomorphic to Dk.
I am totally lost here. I know in Dihedral group, r^n=e=s^2, srs=r^-1. However, I don't know how to proceed this question.
abstract-algebra
asked Nov 19 '18 at 4:50
RandomThinker
192
Let k be an integer such that k divides n. Show that H = is a normal subgroup of Dn (Dihedral group). Then, show that Dn/H is isomorphic to Dk.
I am totally lost here. I know in Dihedral group, r^n=e=s^2, srs=r^-1. However, I don't know how to proceed this question.
abstract-algebra
abstract-algebra
asked Nov 19 '18 at 4:50
RandomThinker
192
asked Nov 19 '18 at 4:50
RandomThinker
192
asked Nov 19 '18 at 4:50
RandomThinker
192
asked Nov 19 '18 at 4:50
RandomThinker
192
asked Nov 19 '18 at 4:50
RandomThinker
192
192
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 '18 at 5:23
add a comment |
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 '18 at 5:23
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 '18 at 5:23
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 '18 at 5:23
add a comment |
active
oldest
votes
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
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3004535%2flet-k-be-an-integer-such-that-k-divides-n-show-that-h-rk-is-a-normal-subgr%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3004535%2flet-k-be-an-integer-such-that-k-divides-n-show-that-h-rk-is-a-normal-subgr%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 '18 at 5:23