User Name Remember Me? Password

 Abstract Algebra Abstract Algebra Math Forum

 May 27th, 2014, 12:31 AM #1 Newbie   Joined: May 2014 From: Montreal Posts: 1 Thanks: 0 Abstract Algebra Sylow Subgroup I have a question about abstract algebra, so if someone could help me answering this question please ... Suppose P,P' are 3-Sylow subgroup, and let Q be their intersection and N the normalizer of Q. Problem: Explain why is the order of N divisible by 9 ? Thanks for your help. Regards, Last edited by skipjack; June 4th, 2014 at 08:00 AM. June 3rd, 2014, 03:46 PM #2 Senior Member   Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra It is not true. For example $A_4$ has distinct Sylow 3-subgroups, e.g. $P=\{e, (123), (132)\}$ and $P'=\{e, (124), (142)\}$, but $|A_4|=12$ so no subgroup of $A_4$ can have an order divisible by $9$. June 4th, 2014, 10:57 AM #3 Senior Member   Joined: Mar 2012 Posts: 294 Thanks: 88 What the OP was probably trying to prove is something like this: Suppose that $|P| = |P'| = 9$, and that $|P \cap P'| = 3$. Then: $9\mid |N_G(P \cap P')|$. In this (special) case, we have that $P,P'$ are abelian, so that: $P \subseteq N(P \cap P')$, since any subgroup of $P$ (or $P'$) is normal in $P$ (respectively, $P'$). The divisibility conclusion then follows by Lagrange. In fact, we can generalize Olinguito's counter-example to any group whose Sylow 3-subgroups have order 3. Thanks from Olinguito Tags abstract, algebra, subgroup, sylow Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post limes5 Abstract Algebra 2 December 31st, 2013 06:06 AM Colocha07 Abstract Algebra 0 May 23rd, 2010 04:52 PM Spartan Math Abstract Algebra 6 September 21st, 2009 09:52 PM Erdos32212 Abstract Algebra 0 December 8th, 2008 06:15 PM weier Abstract Algebra 1 November 20th, 2006 10:40 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      