suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

We give an estimate for the width of congruence subgroup SL(n,OS,I) in Tits–Vaserstein generators, where OS is a localization ring integers number field K. assume that either K has real embedding, or ideal I prime to roots unity

generalization of Rosenfeld's fuzzy subgroup, and Bhakat and Das's fuzzy subgroup is given in [20]. Lie algebras are so-named in honor of Sophus Lie, a Norwegian mathematician who pioneered the study of these mathematical objects. Lie's discovery was tied to his investigation of continuous transformation groups and symmetries. The structure of the laws in physics is largely based on symmetries....

Pediatric traumatic limb amputations are rare and their acute and long term management can be challenging in this subgroup of patients. The lengthy and costly hospital stays, and resulting physical and psychological implications leads to significant morbidity. We present a summary of treatment principles and the evidence base supporting the management options for this entity. The initial manage...

Let RA be a group ring of an abelian group A and let I be an ideal of RA . We say that a subgroup B of A controls I if I = (I ∩ RB)RA. The intersection c(I) of all subgroups of A controlling I is said to be the controller of the ideal I ; c(I) is the minimal subgroup of A which controls the ideal I . The ideal I is said to be faithful if I = A ∩ (1 + I) = 1. In theorem 4 we consider some method...

In this paper we introduce and study an algebraic structure, namely Grouplike. A grouplike is something between semigroup and group and its axioms are generalizations of the four group axioms. Every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). The first idea of grouplikes comes from b-parts and $b$-addition of real number...

Gu map-1 is a modified version of GGH map. It uses same ideal lattices for constructing the trapdoors, while the novelty is that no encodings of zero are given. In this short paper we show that Gu map-1 cannot be used for the instance of witness encryption (WE) based on the hardness of 3-exact cover problem. That is, if Gu map-1 is used for such instance, we can break it by soving a combined 3-...

An absolute ideal of an Abelian group G is a subgroup that in every ring whose additive coincides with G. We describe reduced algebraically compact groups admit at least one structure R such (Problem 93 L. Fuchs’ book “Infinite Groups”). Reduced, compact, have only fully invariant subgroups as are characterized.

Let G be a nite group, F a eld whose characteristic p divides the order of G and A G the invariant ring of a nite-dimensional FG-module V. In analogy to modular representation theory we deene for any subgroup H G the (relative) trace-ideal A G H /A G to be the image of the relative trace map t G X is always a proper ideal of A G ; in fact, we show that its height is bounded above by the codimen...