Let $ G$ be a finite group. Suppose $ K>1$ is a normal proper subgroup of $ G$ with $ K$ abelian. Then we have a new group $ \widetilde{G}=G/K\ltimes K$ . QUESTION: $ G\cong\widetilde{G}$ ? If it is wrong, then what is the relationship on these groups. I want know some information (papers, booksRead more
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