How do i show that $D_6$ has an element of order 6 but $A_4$ has only elements of order 3 and 2 and thus, $A_4$ is not isomorphic to $D_6$? Can someone explain to me? Thanks!
Asked
Active
Viewed 1,460 times
1
-
$D_6$ is the group of symmetries of the hexagon? That is, has order $12$? – lhf Apr 05 '16 at 01:42
-
yes $D_6$ and $A_4$ both have order 12 – eeeeeee Apr 05 '16 at 01:44
1 Answers
1
$D_6$ is the group of symmetries of the hexagon. The $60$-degree rotation is in $D_6$ and has order $6$.
However, no element of $S_4$ has order $6$. See also Element structure of symmetric group:S4.
