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Let $H_1 , H_2 , ... , H_k $ be subgroups of $G$ and $x_1,x_2,... ,x_k$ be elements of $G$ such that $G=\cup_{i=1}^k x_iH_i$ , then how do we prove that some subgroup $H_i$ has finite index in $G$ ?

Asaf Karagila
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Souvik Dey
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  • What role plays $H_1,..., H_k$ in the conditions of $G$? It should not have an $H_k$ instead $H$? – EQJ Sep 11 '14 at 13:24

1 Answers1

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This question has been already treated both here and on mathoverflow. An answer in the latter page points to what I understand to be the first proof of this result as (4.1) and (4.2) in this paper of B.H. Neumann.

Community
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Andreas Caranti
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