Talk:Zassenhaus lemma

[Untitled]

I added a condition that B and D are normal subgroups of A and C, using the usual triangle notation. I'd be surprised if this is not a necessary condition for the conclusion to hold. Please correct if original formulation was actually correct.

Perhaps the article should explicitly state in words which subgroups are normal subgroups of others. For example, one of the conclusions of the lemma is that $B(A\cap D)$ is a normal subgroup of $B(A\cap C)$ (which is currently implicit in the notation because of the quotient notation). Saying this in words provides somebody learning group theory a way to look up the meaning, of say normal subgroup, elsewhere in wikipedia, which notation is not as convenient for.

Although it's rather obvious, the article could emphasize that the butterfly showing the Hasse diagram is upside down in the sense that smaller subgroups are higher. DRLB (talk) 15:42, 9 April 2008 (UTC)

Characters

In my opinion one of the following formulaes from the two isomorphic groups is wrong

   (A\cap C)B/(A\cap D)B is isomorphic to (A\cap C)D/(B\cap C)D. 

I think the first one must be changed to

   B(A\cap C)/B(A\cap D)

in order to coincide with the graph. I am not capable of changing the symbols so I ask you,(the next capable reader of this post) to do so. Thanks. 129.132.211.6 (talk) 13:24, 4 April 2013 (UTC)

Maybe the graph is wrong? The External Link's formulation of the lemma seems to coincide with what is stated in the text, not the graph (switching factors on both sides, which is equivalent AFAICS). --Roentgenium111 (talk) 22:04, 26 May 2013 (UTC)

Cute, but

Despite the cuteness of the butterfly, it actually obscures the mathematical content. In Cohn's _Classic Algebra_ the proof is much more obvious visually by drawing the parallelograms properly which illustrate the application of the second isomorphism theorem. Also, drawing the lattice upside down as it's done here (joins at bottom) than it's usually drawn (joins at the top) is a bit confusing as well. 86.127.138.67 (talk) 04:38, 17 April 2015 (UTC)

External links modified

Hello fellow Wikipedians,

I have just modified one external link on Zassenhaus lemma. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Added archive http://web.archive.org/web/20080604141650/http://www.artofproblemsolving.com:80/Wiki/index.php/Zassenhaus%27s_Lemma to http://www.artofproblemsolving.com/Wiki/index.php/Zassenhaus%27s_Lemma

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{Sourcecheck}}).

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 18 January 2022).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 08:22, 21 July 2016 (UTC)