Generalized Sylow tower groups. II

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 ...

Sylow Theory for Quasigroups Ii: Sectional Action

The first paper in this series initiated a study of Sylow theory for quasigroups and Latin squares, based on orbits of the left multiplication group. The current paper is based on socalled pseudo-orbits, which are formed by the images of a subset under the set of left translations. The two approaches agree for groups, but differ in the general case. Subsets are described as sectional if the pse...