Comments on: Free Groups, Generators, and Relations
https://thetwomeatmeal.wordpress.com/2010/11/15/free-groups-generators-and-relations/
and the Two Meat MealTue, 28 Dec 2010 12:33:07 +0000
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By: Subgroups of Free Groups are Free « Gracious Living
https://thetwomeatmeal.wordpress.com/2010/11/15/free-groups-generators-and-relations/#comment-101
Tue, 28 Dec 2010 12:33:07 +0000http://thetwomeatmeal.wordpress.com/?p=191#comment-101[…] post for a while. As I promised quite a while back, let’s prove together that subgroups of free groups are free. It’s surprising that this is nontrivial to prove: just try to come up with some […]
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By: Symmetric Groups « Gracious Living
https://thetwomeatmeal.wordpress.com/2010/11/15/free-groups-generators-and-relations/#comment-99
Sat, 18 Dec 2010 16:36:28 +0000http://thetwomeatmeal.wordpress.com/?p=191#comment-99[…] fact, they do. Here’s a somewhat lengthy proof. Let , say, be the group generated by this presentation, that is, the group where is always at least . Since satisfies the same relations as , […]
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By: More Products of Groups « Gracious Living
https://thetwomeatmeal.wordpress.com/2010/11/15/free-groups-generators-and-relations/#comment-70
Sun, 28 Nov 2010 03:40:21 +0000http://thetwomeatmeal.wordpress.com/?p=191#comment-70[…] family of groups. Dual to the direct product is the free product, which generalizes the idea of a free group. The amalgamated free product is just a free product that we neutralize on the image of some map. […]
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By: Banach-Tarski part 1 « Gracious Living
https://thetwomeatmeal.wordpress.com/2010/11/15/free-groups-generators-and-relations/#comment-58
Sun, 21 Nov 2010 11:34:05 +0000http://thetwomeatmeal.wordpress.com/?p=191#comment-58[…] now let’s get a little more abstract. Remember when we talked about free groups? It turns out that the free group on two generators, , is paradoxical under its action on itself. […]
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By: Group Actions « Gracious Living
https://thetwomeatmeal.wordpress.com/2010/11/15/free-groups-generators-and-relations/#comment-51
Tue, 16 Nov 2010 20:01:18 +0000http://thetwomeatmeal.wordpress.com/?p=191#comment-51[…] 16 11 2010 Today we’re going to take the abstract group machinery we’ve been building up, and unleash it on some sets. When mathematicians say that “groups describe symmetry,” […]
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