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.

The dihedral group Dn of order 2n has a subgroup of rotations of order n and a subgroup of order 2. Explain why Dn cannot be isomorphic to the external direct product of two such groups.

Please suggest how to go about it.

If H denotes the subgroup of rotations and G denotes the subgroup of order 2.

G = { identity, any reflection} ( because order of any reflection is 2)

I can see that order of Dn = 2n = order of external direct product

share|improve this question

1 Answer 1

up vote 7 down vote accepted

${D}_n \not\cong \mathbb{Z}/2 \oplus \mathbb{Z}/n,$ as the latter is Abelian and the former is not.

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.