Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

For each integer $k\geq 3$, give an example of a finite group $G$ and a subgroup $H$ such that $|G|=k|H|$ and $H$ is not normal in $G$.

I think the case that $k=|G|$ is not considered here.

I have doubts about the way this question is asked; by Lagrange's theorem, not every $3\leq k<|G|$ can give a respective subgroup.

share|improve this question
1  
The question gives us the power to construct the groups G and H, hence your concern that $k = |G|$ is misplaced. –  Calvin Lin Dec 30 '12 at 3:08

1 Answer 1

Hint: Consider dihedral groups of suitable orders and remember that reflections do not generate normal subgroups in dihedral groups.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.