Regular orbits of symmetric and alternating groups

Regular polytopes with symmetric and alternating groups

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.

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)...

Regular Character Tables of Symmetric Groups

We generalize a well-known result on the determinant of the character tables of finite symmetric groups. It is a well-known fact that ifXn is the character table of the symmetric group Sn, then the absolute value of the determinant of Xn equals an, which is defined as the product of all parts of all partitions of n. It also equals bn, which is defined as the product of all factorials of all mul...

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.