Solution Found!
If n 4 and is even, show that Dn has exactly n/2 noncyclic
Chapter 4, Problem 79E(choose chapter or problem)
QUESTION:
If \(n \geq 4 \) and is even, show that \(D_n\) has exactly n/2 noncyclic subgroups of order 4.
Questions & Answers
QUESTION:
If \(n \geq 4 \) and is even, show that \(D_n\) has exactly n/2 noncyclic subgroups of order 4.
ANSWER:Step 1 of 3
Let us consider thatis even.
The dihedral grouphasrotations namely andhasreflections namely.
It is given that is even, belongs to.
The subsets of the form are closed under the composition.
Sois a non-cyclic subgroup of order four of, whenis even, and hereis a reflection.