On the exponent of N m K 2 ( $\mathbb{F}$ [ C p n ])

Let C p n be the cyclic p -group of order p n and $\mathbb{F}$ a finite field of characteristic p . For any integer 1 ≤ l ≤ n , we obtain infinitely many non-trivial elements of order p l in N m K 2 ( $\mathbb{F}$ [ C p n ]). In fact, these elements form a generating set of N m K 2 ( $\mathbb{F}$ [ C p n ]) and the exponent of N m K 2 ( $\mathbb{F}$ [ C p n ]) is p n .