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A note on the torsion elements in the centralizer of a finite index subgroup. (English) Zbl 0867.20022

Let \(H\) be any subgroup of finite index in a given group \(G\) and \(T\) be the set of torsion elements of the centralizer \(C_G(H)\) of \(H\) in \(G\). The author proves that \(T\) is a subgroup of \(G\). Moreover it is shown that if \(H\) is torsion free and normal then \(T\) is the unique maximal normal torsion subgroup of \(G\).

MSC:

20E07 Subgroup theorems; subgroup growth
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