Suppose that H and K are subgroups of a group G. Give an example that HK may not be a subgroup of G.

I believe that a Dihedral group would work but I'm not entirely sure.

Question

Suppose that H and K are subgroups of a group G. Give an example that HK may not be a subgroup of G. 

I believe that a Dihedral group would work but I'm not entirely sure.

zarkon · Answer

if you believe that is the case...what would you use for H and K?  Try a few and see if it works

anonymous · Answer

um....maybe D3 as G and then H contains the identity and a a flip about a symmetry while K contains the identity and another flip about a symmetry...? Then if those two are multiplied together it will have four distinct elements but that can't be because G has six elements and 4 doesn't divide 6.

I think this could work? I just wanna make sure.