tag:blogger.com,1999:blog-12604614.post114931307342937113..comments2018-04-04T12:16:24.151-07:00Comments on Math Refresher: Group Theory: Lagrange's TheoremLarry Freemanhttp://www.blogger.com/profile/06906614246430481533noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-12604614.post-82608571862312133852012-04-23T06:54:54.562-07:002012-04-23T06:54:54.562-07:00This comment has been removed by a blog administrator.Pawan Seerwanihttps://www.blogger.com/profile/03166679966160204233noreply@blogger.comtag:blogger.com,1999:blog-12604614.post-9718357366603921322012-04-23T06:51:13.818-07:002012-04-23T06:51:13.818-07:00This post helped me a lot..!!
Thanks and keep wri...This post helped me a lot..!! <br />Thanks and keep writing..! :) :)Pawan Seerwanihttps://www.blogger.com/profile/03166679966160204233noreply@blogger.comtag:blogger.com,1999:blog-12604614.post-23018615093024796572011-12-04T22:33:51.466-08:002011-12-04T22:33:51.466-08:00Hi Novita,
Can you provide more details on your e...Hi Novita,<br /><br />Can you provide more details on your example. I'm not clear how you are getting to O(G)=9.<br /><br />Are you sure that you are following this assumption:<br /><br />From this, we know that the set of cosets can be divided up as follows: a1H, a2H, ..., arH where r is a positive integer and where for each coset i ≠ j → aiH ∩ ajH = ∅<br /><br />-LarryLarry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.comtag:blogger.com,1999:blog-12604614.post-49025040138104971502011-12-04T18:34:23.588-08:002011-12-04T18:34:23.588-08:00hi,
thanks for your explanation,,
the first time i...hi,<br />thanks for your explanation,,<br />the first time i read the proof in the book contemporary abstract algebra,n when i read your explanation i understand about the proof but i still confused about steps 6 order(G)= order(a1(H))+....order(ar(H))if we sum like that so relation with your example before o(G)=o(0(H))+o(1(H))...+o(8(H))=3+3+3+3+3+3+3+3=24.it is wrong,because o(G)=9<br />and then steps 7 o(G)= r.o(H) relation with example r=8 so o(G)=8.3=24.<br />please explain that i need that in this week..novitahttps://www.blogger.com/profile/05193334350105002939noreply@blogger.comtag:blogger.com,1999:blog-12604614.post-36993877283935782062011-03-13T07:40:59.800-07:002011-03-13T07:40:59.800-07:00GOD !!!GOD !!!paajihttps://www.blogger.com/profile/09187691829645847141noreply@blogger.comtag:blogger.com,1999:blog-12604614.post-61046655134044775832010-05-06T14:48:56.723-07:002010-05-06T14:48:56.723-07:00Very well exlained. This note on lagrange theorem ...Very well exlained. This note on lagrange theorem in group theory helped me more than my textbook.<br />Thanks!!!Manohar Kusehttps://www.blogger.com/profile/05590836757836705107noreply@blogger.comtag:blogger.com,1999:blog-12604614.post-27290806237010760512009-01-22T08:00:00.000-08:002009-01-22T08:00:00.000-08:00Thank you, that made it clear!Thank you, that made it clear!Tomnoreply@blogger.comtag:blogger.com,1999:blog-12604614.post-67707780765654621542009-01-21T21:54:00.000-08:002009-01-21T21:54:00.000-08:00Hi Tom,I'll try to break it down step by step....Hi Tom,<BR/><BR/>I'll try to break it down step by step. I hope that this makes the step clear.<BR/><BR/>In Lemma 2, step #3 says that:<BR/>x = bh_2<BR/>x = ah_1<BR/><BR/>Since x=ah_1, we know that:<BR/>a = x(h_1)^(-1)<BR/><BR/>Since x=bh_2, we know that:<BR/>x(h_1)^(-1) = (bh_2)(h_1)^(-1)<BR/><BR/>Since a = x(h_1)^(-1), it follows that:<BR/>a = (bh_2)(h_1)^(-1)<BR/><BR/>Since a=(bh_2)(h_1)^(-1), it follows that:<BR/>aH=[(bh_2)(h_1)^(-1)]H<BR/><BR/>We further note that:<BR/>[(bh_2)(h_1)^(-1)]H = b[(h_2)(h_1)^(-1)H]<BR/><BR/>Now, we know that h_1,h_2 are elements of H [from step #3]<BR/><BR/>Since h_1 ∈ H, it follows that (h_1)^(-1) ∈ H. [Since closure is a property of groups]<BR/><BR/>Since (h_1)^(-1) ∈ H and h_2 ∈ H, it follows that (h_2)(h_1)^(-1) ∈ H<BR/><BR/>That's all we need to use Lemma 1 above. Since (h_2)(h_1)^(-1) ∈ H, <BR/>[(h_2)(h_1)^(-1)]H = H<BR/><BR/>Since [(h_2)(h_1)^(-1)]H = H, it follows that:<BR/>b[(h_2)(h_1)^(-1)]H = bHLarry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.comtag:blogger.com,1999:blog-12604614.post-51036265678505276432009-01-21T16:27:00.000-08:002009-01-21T16:27:00.000-08:00Hi Larry,On your page about the proof of Lagrange ...Hi Larry,<BR/><BR/>On your page about the proof of Lagrange theorem at<BR/><BR/>http://mathrefresher.blogspot.com/2006/06/group-theory-lagranges-theorem.html<BR/><BR/>can you explain how step 5 in Lemma 2 follows from Lemma 1? I'm not sure I understood.Tomnoreply@blogger.comtag:blogger.com,1999:blog-12604614.post-58993898100541150722008-04-13T07:40:00.000-07:002008-04-13T07:40:00.000-07:00Hi Larry,It was wonderful going thru ur blog. You ...Hi Larry,<BR/><BR/>It was wonderful going thru ur blog. You really have maintained it in an impeccable manner - i must say. Further, you have gone thru the troubles of providing links for some concepts which others might need and again it is a wonderful act and i really appreciate it. The world needs more math afficiandos like you.<BR/><BR/>Thanks for your beautiful explanations. Again I add thanks for your selfless service to humanity....Hope you create a book out of your blogs.Akashhttps://www.blogger.com/profile/06989706264146599229noreply@blogger.com