Prove that the dihedral groups $D_n$ are all Lagrangian

Question

I was reading a book on group theory and there was problem in the book that states:

Prove that the dihedral groups $D_n$ are all Lagrangian for $n\geq3$.

Apologies the previous hint was not for this question.

If anyone could answer this question is would be hugely appreciated.

What definition of $D_n$ are you using? Which book are you referring to? — Shaun, Jan 17 '20 at 17:52
You are new, so you may not know: do not remove content like you just did; especially when there is already an answer to the question. — Arturo Magidin, Jan 17 '20 at 17:58

score 1 · Answer 1 · answered Jan 17 '20 at 17:52

1

All dihedral groups are supersolvable and hence Lagrangian, i.e., the converse of Lagrange's theorem holds.

References:

answered Jan 17 '20 at 17:52

Dietrich Burde

1 Answers1