Consider the group $G:=A⋊_{f}B$. Let $G$ act on the set of left cosets for $B$, inducing the permutation representation $\theta:G→S_n$.
Can we conclude that $|\theta(G)|=|\theta(A)||\theta(B)|$?
2026-03-29 14:31:25.1774794685
Order of Image of Semidirect Product under Left Regular Representation
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