On generalizations of Sylow tower groups

Sylow Groups of Groups of Polynomial Permutations

We enumerate and describe the Sylow p-groups of the group of polynomial permutations of the integers mod p . MSC 2000: primary 20D20, secondary 11T06, 13M10, 11C08, 13F20, 20E18.

POS-groups with some cyclic Sylow subgroups

A finite group G is said to be a POS-group if for each x in G the cardinality of the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups with some cyclic Sylow subgroups.

Finite Groups with p-Sylow Coverings

The Sylow Subgroups of the Symmetric Groups

The aim of this paper is to give a direct approach to the study of the Sylow ^-subgroups Sn of the symmetric group of degree pn. [We assume throughout that p^2.] Many of the results are already known and are treated in a paper by Kaloujnine where he uses a particular representation by means of "reduced polynomials."1 It has seemed worth while to restate some of his results using the concept of ...

On rational groups with Sylow 2-subgroups of nilpotency class at most 2

A finite group $G$ is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on $G$ and also via nilpotency and nonnilpotency assumption of $G$.