–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.

By the Artin Induction theorem,C(G) is a finite abelian group with exponent dividing the order of G. Some work on this sequence has already been done. In [14] and [16], Ritter and Segal proved that C(G) = 0 for G a finite p–group. Serre [17, p. 104] remarked that C(G) / = 0 for G = Z/3 × Q8 (the direct product of a cyclic group of order 3 and a quaternion group of order 8). Berz [2] gave a nice...

We survey three methods for proving that the characteristic polynomial of a finite ranked lattice factors over the nonnegative integers and indicate how they have evolved recently. The first technique uses geometric ideas and is based on Zaslavsky’s theory of signed graphs. The second approach is algebraic and employs results of Saito and Terao about free hyperplane arrangements. Finally we con...

Leibniz algebras are a non-anticommutative version of Lie algebras. They play an important role in different areas mathematics and physics have attracted much attention over the last thirty years. In this paper we investigate whether conditions such as being algebra, cyclic, simple, semisimple, solvable, supersolvable or nilpotent algebra preserved by lattice isomorphisms.

One way to view Theorem 1.1 is as a statement that the algebraic structure of a finitely generated profinite group somehow also encodes the topological structure. That is, if one wishes to know the open subgroups of a profinite group G, a topological property, one must only consider the subgroups of G of finite index, an algebraic property. As profinite groups are compact topological spaces, an...

Comparing two expressions of the Tutte polynomial of an ordered oriented matroid yields a remarkable numerical relation between the numbers of reorientations and bases with given activities. A natural activity preserving reorientation-to-basis mapping compatible with this relation is described in a series of papers by the present authors. This mapping, equivalent to a bijection between regions ...

let $g={rm sl}_2(p^f)$ be a special linear group and $p$ be a sylow‎ ‎$2$-subgroup of $g$‎, ‎where $p$ is a prime and $f$ is a positive‎ ‎integer such that $p^f>3$‎. ‎by $n_g(p)$ we denote the normalizer of‎ ‎$p$ in $g$‎. ‎in this paper‎, ‎we show that $n_g(p)$ is nilpotent (or‎ ‎$2$-nilpotent‎, ‎or supersolvable) if and only if $p^{2f}equiv‎ ‎1,({rm mod},16)$‎.

in this paper we find systems of subgroups of a finite‎ ‎group‎, ‎which $bbb p$-subnormality guarantees supersolvability‎ ‎of the whole group‎.