## 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:

 2e+08 Subgroup theorems; subgroup growth
Full Text: