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Let $G$ be a group and $H$ be a subgroup of finite index. Prove that there is only a finite number of distinct subgroups in $G$ of the form $gHg^{-1}$ where $g$ belongs to $G$.

Ali Caglayan
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Zonash ali
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1 Answers1

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HINT: If $g'\in gH$, what can you say about $g'H(g')^{-1}$?

Brian M. Scott
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