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Questions about the branch of algebra that deals with groups.

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Free partners in semi-direct products

Let $G = N \rtimes K$ be a semi-direct product of groups and suppose that $K$ is a finite group. Call the set $\mathcal{F} = \{ \alpha \in G \mid \langle \alpha, K \rangle = \langle \alpha \rangle \as …
Doryan Temmerman's user avatar