Which property describes the multiplicative group (Z/2kZ)∗(\mathbb{Z}/2^k\mathbb{Z})^*(Z/2kZ)∗ for k≥3k \ge 3k≥3?
C2×C2k−2C_2 \times C_{2^{k-2}}C2×C2k−2
Cyclic group C2k−1C_{2^{k-1}}C2k−1
C4×C2k−3C_4 \times C_{2^{k-3}}C4×C2k−3
Elementary abelian group