My Math Forum About minimal normal groups and subnormal groups

 Abstract Algebra Abstract Algebra Math Forum

 October 20th, 2011, 09:45 AM #1 Newbie   Joined: Oct 2011 Posts: 1 Thanks: 0 About minimal normal groups and subnormal groups Hello everybody, I would like to have some help with these two questions: 1. Let $G$ be a finite nilpotent group and $N$ a minimal normal subgroup. Show that $N\leq Z(G)$. 2. Let $G$ be a group and $S,T$ verifying $S\neq T$ non-abelian subnormal subgroups of $G$. Prove that $st=ts$ $\forall s\in S$ $\forall t\in T$ 1. I have already proved that $N$ must be abelian; $N\leq Z(N)$, but I find no way of proving that $N\leq Z(G)$ using that the nilpotency of $G$ and each one of its characterizations. Any idea? Regards and thanks in advance. Sheila.

 Tags groups, minimal, normal, subnormal

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Math Amateur Abstract Algebra 0 October 29th, 2013 03:46 PM tiger4 Abstract Algebra 2 April 18th, 2012 01:13 PM SonicYouth Abstract Algebra 3 March 13th, 2011 12:31 AM lime Abstract Algebra 3 October 25th, 2010 07:30 AM cashimingo Abstract Algebra 3 December 23rd, 2008 11:54 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top