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Apr 8, 2021 at 9:50 comment added A.Messab @DerekHolt thank you very much professor, it is indeed a counterexample.
Apr 6, 2021 at 22:33 comment added Derek Holt Suppose we let $G = C_2 \times C_2$ be a Klein $4$-group and $H$ and $N$ distinct subgroups of order $2$. Is that not a counterexample? The transfer map is $g \mapsto g^2$, so the image is trivial.
Apr 6, 2021 at 22:14 comment added A.Messab $N^2$ is the subgroup generated by all the squares of $N$, the same thing for $H^2$.
Apr 6, 2021 at 22:04 comment added Derek Holt What do $N^2$ and $H^2$ mean?
Apr 6, 2021 at 17:08 history asked A.Messab CC BY-SA 4.0