Semi-automorphisms of symmetric and alternating groups

Automorphisms of Quotients of Symmetric Groups

We describe the automorphism group of the quotient of the symmetric group on a countably innnite set by the group of nitary permutations. We show that the outer automorphism group is innnite cyclic. In the proof, we examine the structure of centralizers in this quotient.

Short presentations for alternating and symmetric groups

We derive new families of presentations (by generators and relations) for the alternating and symmetric groups of finite degree n. These include presentations of length that are linear in log n, and 2-generator presentations with a bounded number of relations independent of n.

Regular polytopes with symmetric and alternating groups

On Alternating and Symmetric Groups as Galois Groups

Fix an integer n = 3. We show that the alternating group An appears as Galois group over any Hilbertian field of characteristic different from 2. In characteristic 2, we prove the same when n is odd. We show that any quadratic extension of Hilbertian fields of characteristic different from 2 can be embedded in an Sn–extension (i.e. a Galois extension with the symmetric group Sn as Galois group)...

finite groups which are the products of symmetric or alternating groups with $l_3(4)$

in this paper‎, ‎we determine the simple groups $g=ab$‎, ‎where $b$ is isomorphic to $l_{3}(4)$ and $a$ isomorphic to an alternating or a symmetric group on $ngeq5$‎, ‎letters‎.