Register to reply 
Simple groups 
Share this thread: 
#1
Mar1211, 06:01 AM

P: 366

What are some simple groups that have nonnormal subgroups? The only example I can think of is the alternating group for n > 4.



#2
Mar1211, 02:27 PM

Sci Advisor
HW Helper
P: 9,488

all non abelian simple groups have non normal subgroups. i.e. they have even order, so they have elements of order 2, hence subgroups of order 2, which are necessarily non normal.



#3
Mar1211, 04:43 PM

P: 366

Thanks for your reply, mathwonk!
I was kind of hoping for some specific examples of known groups. The only examples of simple groups with which I'm familiar are [itex] \mathbb{Z}/p\mathbb{Z}[/itex] and [itex]A_n[/itex] for n > 4. Are there any other wellknown ones? Thanks again! 


#4
Mar1211, 05:12 PM

Mentor
P: 18,327

Simple groups



#5
Mar1311, 07:20 AM

P: 366




Register to reply 
Related Discussions  
Group Theory Question involving nonabelian simple groups and cyclic groups  Calculus & Beyond Homework  1  
Simple Abelian groups  Linear & Abstract Algebra  1  
Normal and Simple groups  Linear & Abstract Algebra  6  
Simple groups  Calculus & Beyond Homework  10  
Groups, order G = 60, G simple  Calculus & Beyond Homework  3 