For a finite group G, subgroup P of G is 2-minimal if B<P, where B=NG(S) for some Sylow 2-subgroup S and B contained in unique maximal P. fields odd characteristic, this paper contains detailed explicit description all the subgroups general orthogonal groups, certain their subgroups.

–Let p be a prime number, G p-solvable finite group and P Sylow p-subgroup of G. We prove that is p-supersolvable if NG(P) there subgroup H with P??H??(P) such s-semipermutable in As applications, we simplify the proofs some known results also generalize results.

The purpose of this note is to determine all endotrivial modules in prime characteristic p, for a finite group having a cyclic Sylow p-subgroup. In other words, we describe completely the group of endotrivial modules in that case. The endotrivial modules are a family of finitely generated modules for a group algebra of a finite group which appear naturally in modular representation theory. Seve...

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...

a subgroup $h$ is said to be $nc$-supplemented in a group $g$ if there exists a subgroup $kleq g$ such that $hklhd g$ and $hcap k$ is contained in $h_{g}$, the core of $h$ in $g$. we characterize the supersolubility of finite groups $g$ with that every maximal subgroup of the sylow subgroups is $nc$-supplemented in $g$.

over a period of three months (summer), 108 samples of water collected from four hospitals in te-hran. they were taken from numerous potable and non-potable water, including main supply cis-terns, calorifiers, hot and cold tap water, shower, cooling tower and drain of air condition system. culturing of concentrated and non-concentrated water samples on buffered charcoal yeast extract (bcye) aga...

Two tournaments T1 and T2 on the same vertex set X are said to be switching equivalent if X has a subset Y such that T2 arises from T1 by switching all arcs between Y and its complement X \ Y . The main result of this paper is a characterisation of the abstract finite groups which are full automorphism groups of switching classes of tournaments: they are those whose Sylow 2-subgroups are cyclic...