5
$\begingroup$

Is there any example for non-Abelian group in which has more than $3$ elements of order $ 2$, but has less than 7 elements of order $2$?

$\endgroup$

2 Answers 2

11
$\begingroup$

Consider $D_4$ Dihedral group, non-abelian, $5$ elements of order $2$.

$\endgroup$
1
  • 2
    $\begingroup$ Also dihedral group with 10 elements works. $\endgroup$ Jan 25, 2015 at 19:13
4
$\begingroup$

The dihedral group of order $8$ - the symmetries of a square is one such.

It has the identity element and two elements of order $4$ (clockwise and counterclockwise quarter turns). The other five elements are four reflections about axes of symmetry and a half turn - all of order 2.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .