Let G be a group with all subgroups subnormal. A normal subgroup N of G is said to be G-minimax if it has a finite G-invariant series whose factors are abelian and satisfy either max-G or minG. It is proved that if the normal closure of every element of G is G-minimax then G is nilpotent and the normal closure of every element is minimax. Further results of this type are also obtained.

We consider amalgamations of nitely generated nilpotent groups of class c. We show that doubles satisfy a polynomial isoperimetric inequality of degree 2c. Generalising doubles we introduce non-twisted amalgamations and show that they satisfy a polynomial isoperimetric inequality as well. We give a su cient condition for amalgamations along abelian subgroups to be non-twisted and thereby to sat...

iodine deficiency is the most important preventable cause of mental deficiency. the aim of this study was to specify the phase during fetal and postnatal development when iodine supplementation would have optimum effect on the prevention of brain damage. materials and methods forty schoolchildren aged 7-13 years, from the previously iodine deficient villages of kiga and randan, were divided int...

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 $p^{2f}equiv‎ ‎1,({rm mod},16)$‎.

for a parabolic subgroup P ⊂ G. In Part I [Na 2], when g is classical, we have proved that any two symplectic resolutions of Ō are connected by a sequence of Mukai flops of type A or of type D. In this paper (Part II), we shall improve and generalize all arguments in Part I so that the exceptional Lie algebras can be dealt with. We shall replace all arguments of [Na 2] which use flags, by those...

We give a necessary condition to reduce the Cayley isomorphism problem for Cayley objects of a nilpotent or abelian group G whose order satisfies certain arithmetic properties to the Cayley isomorphism problem of Cayley objects of the Sylow subgroups of G in the case of nilpotent groups, and in the case of abelian groups to certain natural subgroups. As an application of this result, we show th...

Let G be a finite group, p a fix prime and P a Sylow p-subgroup of G. In this short note we prove that if p is odd, G is p-nilpotent if and only if P controls fusion of cyclic groups of order p. For the case p = 2, we show that G is p-nilpotent if and only if P controls fusion of cyclic groups of order 2 and 4.

Introduction: Non-target radiation effects are damages and effects that occur without the need for direct radiation exposure in cells. Bystander signals cause non-targeted irradiation effect that has been defined as radiation responses in which non-irradiated cells exhibit irradiated effects as a result of signals from adjacent irradiated cells. In this study, the bystander ef...

We study properties and the structure of Cartan subgroups in a connected Lie group. obtain characterisation which generalises W\"ustner's theorem for same. show that are same as those centralizers maximal compact radical. Moreover, we describe recipe constructing containing certain nilpotent solvable characterise quotient group modulo closed normal subgroup images ambient also density power map...

Abstract Suppose that ???? is a class of groups consisting only periodic and P ? ( mathvariant="script">C stretchy="false">) ? \mathfrak{P}(\mathcal{C})^{\prime} the set prime numbers do not...