Given G: group of units in Z mod 14 under multiplication. A function sends the integers under addition to G.
$f(n)$ = $[3]^n$
I am just checking whether I am correct in stating that the kernel is simply the order which would be 6 and this would represented as <6>.
$f(6n)=[3]^{6n}=[729]^n=[1]^n=[1]$
Or if you want to be more pedantic, you can show that if $x\in \ker(f)$ then $x=6k$ for some $k\in \mathbb{Z}$. Suppose not, then write $x$ as $6k+j$ where $j\in \{1,2,3,4,5\}$. Calculation should be straightforward.