
#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: 9,421

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: 16,583

Simple groups 



#5
Mar1311, 07:20 AM

P: 366




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