Maurer, Iulius Gyula A topology on the group of infinite permutations. (Eine Topologisierung der Gruppe unendlicher Permutationen.) (Romanian. Russian, German summaries) Zbl 0075.01601 Acad. Republ. Popul. Romîne, Bul. Şti., Secţ. Şti. Mat. Fiz. 8, 265-272 (1956). In the group of all one to one applications of a countable set \(N\) onto itself, it is first introduced the concept of the limit of a sequence. Namely: \(\pi_n\to\pi\) if, for every \(k\in N\), it exists a natural \(R\) such that \(\pi_n(k)\to \pi(k)\) for \(n > R\). It is shown that this convergence induces in the usual way a topology, compatible with the group structure. Let \(S_{\infty}^t\) be the constructed topology group. It is shown that the group of finite permutations (i.e. of those applications for which the set of non invariant points is finite) is dense in \(S^t_{\infty}\). It is also shown that \(S^t_{\infty}\) has no invariant closed subgroups and that all its automorphisms are inner. Reviewer: Ion Cuculescu (Bucureşti) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page MSC: 22A99 Topological and differentiable algebraic systems 20B07 General theory for infinite permutation groups Keywords:Group theory PDFBibTeX XMLCite \textit{I. G. Maurer}, Acad. Republ. Popul. Romîne, Bul. Ști., Secț. Ști. Mat. Fiz. 8, 265--272 (1956; Zbl 0075.01601)