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

Dekimpe, Karel

Bull. Belg. Math. Soc. - Simon Stevin 3, No. 5, 497-500 (1996).

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 \(G\).

Reviewer: A.I.Budkin (Barnaul)

MSC:

20E07

Subgroup theorems; subgroup growth

Keywords:

subgroups of finite index; sets of torsion elements; centralizers; maximal normal torsion subgroups