The absolute centre of a group
The absolute centre of a group \(G\) is the subgroup \(L(G)\) of all elements of \(G\) which are fixed by every automorphism of \(G\), and the auto-commutator subgroup of \(G\) is the subgroup \(G^*\) generated by all products \(g^{-1}g^\alpha\), where \(g\) is in \(G\) and \(\alpha\) is any automorphism of \(G\). The author proves that if \(G/L(G)\) is finite, then also \(G^*\) and \(\Aut\,G\) are finite. He also gives bounds for the orders of \(G^*\) and \(\Aut\,G\) in terms of the order of \(G/L(G)\).
scientific article; zbMATH DE number 701286