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Expositions of interesting mathematical resultsMon, 08 May 2017 10:02:45 +0000hourly1http://wordpress.com/Comment on Groups and Group Actions: Lecture 12 by Groups and Group Actions: Lecture 13 | Theorem of the week
https://theoremoftheweek.wordpress.com/2017/05/03/groups-and-group-actions-lecture-12-2/#comment-7263
Mon, 08 May 2017 10:02:45 +0000http://theoremoftheweek.wordpress.com/?p=2765#comment-7263[…] Expositions of interesting mathematical results « Groups and Group Actions: Lecture 12 […]
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Mon, 08 May 2017 10:02:43 +0000http://theoremoftheweek.wordpress.com/?p=2632#comment-7262[…] Theorem 59 (Orbit-Stabiliser Theorem): Let be a finite group acting on a set . Take . Then . We defined a map from to and showed that it’s a bijection, then used Lagrange’s theorem. […]
]]>Comment on Groups and Group Actions: Lecture 7 by Groups and Group Actions: Lecture 12 | Theorem of the week
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Wed, 03 May 2017 10:07:08 +0000http://theoremoftheweek.wordpress.com/?p=2610#comment-7246[…] Proposition 56: The orbits of an action partition the set. We defined an equivalence relation whose equivalence classes are precisely the orbits, and were then done by Theorem 27. […]
]]>Comment on Theorem 26: the first isomorphism theorem by Groups and Group Actions: Lecture 11 | Theorem of the week
https://theoremoftheweek.wordpress.com/2010/05/20/theorem-26-the-first-isomorphism-theorem/#comment-7244
Mon, 01 May 2017 10:07:14 +0000http://theoremoftheweek.wordpress.com/?p=566#comment-7244[…] long time ago, I wrote something about the first isomorphism theorem. There’s also a more recent hedgehogmaths […]
]]>Comment on Groups and Group Actions: Lecture 8 by Groups and Group Actions: Lecture 11 | Theorem of the week
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Mon, 01 May 2017 10:07:10 +0000http://theoremoftheweek.wordpress.com/?p=2632#comment-7243[…] 55: Let be a finite group, let be a group, let be a homomorphism. Then . We used our proof of Lagrange’s theorem, which showed that if then […]
]]>Comment on Groups and Group Actions: Lecture 10 by Groups and Group Actions: Lecture 11 | Theorem of the week
https://theoremoftheweek.wordpress.com/2017/04/26/groups-and-group-actions-lecture-10-3/#comment-7242
Mon, 01 May 2017 10:07:08 +0000http://theoremoftheweek.wordpress.com/?p=2718#comment-7242[…] Expositions of interesting mathematical results « Groups and Group Actions: Lecture 10 […]
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Wed, 26 Apr 2017 11:48:48 +0000http://theoremoftheweek.wordpress.com/?p=2632#comment-7237[…] and takes different values on different cosets. We saw that if and only if , and then used the coset equality test to see that this is equivalent to […]
]]>Comment on Groups and Group Actions: Lecture 5 by Groups and Group Actions: Lecture 10 | Theorem of the week
https://theoremoftheweek.wordpress.com/2017/03/01/groups-and-group-actions-lecture-5-3/#comment-7236
Wed, 26 Apr 2017 11:48:45 +0000http://theoremoftheweek.wordpress.com/?p=2546#comment-7236[…] We proved this using the subgroup test. […]
]]>Comment on Groups and Group Actions: Lecture 7 by Groups and Group Actions: Lecture 9 | Theorem of the week
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Mon, 24 Apr 2017 10:10:26 +0000http://theoremoftheweek.wordpress.com/?p=2610#comment-7235[…] that are self-inverse — ) or 2 (). By counting the number of each, and remembering that equivalence classes partition the set, we saw that the number of classes of size 1 is even. Since it’s also at least 1, there must be […]
]]>Comment on Groups and Group Actions: Lecture 6 by Groups and Group Actions: Lecture 9 | Theorem of the week
https://theoremoftheweek.wordpress.com/2017/03/02/groups-and-group-actions-lecture-6-3/#comment-7234
Mon, 24 Apr 2017 10:10:24 +0000http://theoremoftheweek.wordpress.com/?p=2583#comment-7234[…] Moreover, if is an isomorphism then . We showed that , and then the first part follows using Lemma 23. For the second part, we noted that for injective we have if and only if […]
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