Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...

we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.

let $h$, $l$ and $x$ be subgroups of a finite group$g$. then $h$ is said to be $x$-permutable with $l$ if for some$xin x$ we have $al^{x}=l^{x}a$. we say that $h$ is emph{$x$-quasipermutable } (emph{$x_{s}$-quasipermutable}, respectively) in $g$ provided $g$ has a subgroup$b$ such that $g=n_{g}(h)b$ and $h$ $x$-permutes with $b$ and with all subgroups (with all sylowsubgroups, respectively) $v$...

In this paper, for a CM abelian extension K/k of number fields, we propose conjecture which describes completely the Fitting ideal minus part Pontryagin dual T-ray class group K set T primes as Gal(K/k)-module. Here, emphasize that consider full group, and do not throw away ramifying (the object study is quotient by subgroup generated classes primes). We prove our consequence equivariant Tamaga...

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

BACKGROUND Advances in molecular technology have shifted new drug development toward targeted therapy for treatments expected to benefit subpopulations of patients. Adaptive signature design (ASD) has been proposed to identify the most suitable target patient subgroup to enhance efficacy of treatment effect. There are two essential aspects in the development of biomarker adaptive designs: 1) an...

OBJECTIVE To investigate (a) the applicability of the proportional recovery rule of spontaneous neurobiological recovery to motor function of the paretic lower extremity (LE); and (b) the presence of fitters and non-fitters of this prognostic rule poststroke. When present, the clinical threshold for fitting nor non-fitting would be determined, as well as within-subject generalizability to the p...

IN this paper we shall study the connection between local and global nilpotency for groups which satisfy certain chain conditions. In the first section, we shall prove that a group satisfying the chain condition on centralizers has a unique maximal normal nilpotent subgroup (the Fitting subgroup), i.e. the group generated by all normal nilpotent subgroups must again be nilpotent. This generaliz...