Note that the intersection property in Theorem A is equivalent to saying that NL(P ) is a p-group. Also, since this property is clearly independent of the choice of P in Sylp(G), it is clear that L is characteristic in G. Our interest in this characteristic subgroup was motivated by the following. Theorem B. Suppose that G is p-solvable and let L be the largest normal subgroup of G such that L∩...

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...

We develop a theory of convex cocompact subgroups of the mapping class group MCG of a closed, oriented surface S of genus at least 2, in terms of the action on Teichmüller space. Given a subgroup G of MCG de ning an extension 1 ! 1(S) ! ΓG ! G ! 1, we prove that if ΓG is a word hyperbolic group then G is a convex cocompact subgroup of MCG. When G is free and convex cocompact, called a Schottky ...

in this paper, we examine that some simple $k_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees.

In this paper we investigate expanding maps on infra-nilmanifolds. Such manifolds are obtained as a quotient E\L, where L is a connected and simply connected nilpotent Lie group and E is a torsion-free uniform discrete subgroup of LoC, with C a compact subgroup of Aut(L). We show that if the Lie algebra of L is homogeneous (i.e., graded and generated by elements of degree 1), then the correspon...

For a graph G, denote by L i (G) its i-iterated line graph and denote by W (G) its Wiener index. We prove that the function W (L i (G)) is convex in variable i. Moreover, this function is strictly convex if G is different from a path, a claw K 1,3 and a cycle. As an application we prove that W (L i (T)) = W (T) for every i ≥ 3 if T is a tree in which no leaf is adjacent to a vertex of degree 2,...

Given a set S of n distinct points { (xi'Yi) 1 0 5 i < n] 9 the convex hull problem is to determine the vertices of the convex hull H(S) . All the known algorithms for solving this problem have a worst-case running time of cn log n or higher, and employ only quadratic tests, i.e., tests of ‘the form f(Xo’YO ⌧19 Yl> l l l ☺ ⌧nBl’ Y, 1> : 0 with f being any polynomial of degree not exceeding 2 . ...

We look at Hopf Galois structures with square free pqw degree on separable field extensions (nonnormal) L/K. Where E/K is the normal closure of L/K, group permutation G = Gal(E/K). study details nonabelian case, where Jl ⟨σ, [τ, αl ]⟩ a regular subgroup Hol(N) for 1 ≤ l w − 1. first find G, and then each G. In this there exists four such that are admissible within