A group is called capable if it is a central factor group. We consider the capability of nilpotent products of cyclic groups, and obtain a generalization of a theorem of Baer for the small class case. The approach is also used to obtain some recent results on the capability of certain nilpotent groups of class 2. We also prove a necessary condition for the capability of an arbitrary p-group of ...

The Bott–Thurston cocycle is a $$2$$ -cocycle on the group of orientation-preserving diffeomorphisms circle. We introduce and study formal analog cocycle. continuous $$A$$ -automorphisms algebra $$A((t))$$ Laurent series over commutative ring with values in $$A^*$$ invertible elements . prove that central extension given by equivalent to 12-fold Baer sum determinantal when $$\mathbb Q$$ -algebr...

Let $\pi$ be a proper subset of the set all primes. Denote by $r$ smallest prime which does not belong to and $m = r$ if $r 2$ or $3$ r-1$ \geqslant 5$. We study following conjecture: conjugacy class $D$ finite group $G$ is contained in $\pi$-radical $\mathrm{O}_\pi(G)$ only every $m$ elements generate $\pi$-subgroup. confirm this conjecture for each whose nonabelian composition factors are iso...

an ideal i of a ring r is called right baer-ideal if there exists an idempotent e 2 r such that r(i) = er. we know that r is quasi-baer if every ideal of r is a right baer-ideal, r is n-generalized right quasi-baer if for each i e r the ideal in is right baer-ideal, and r is right principaly quasi-baer if every principal right ideal of r is a right baer-ideal. therefore the concept of baer idea...

Boolean powers were introduced by Foster [5]. It was noticed by Jónsson in the review of [6], and further elaborated by Banaschewski and Nelson [1], that the Boolean power of an algebra A by a Boolean algebra B can be described as the algebra of continuous functions from the Stone space of B to A, where A has the discrete topology. It follows that a Boolean power of the group Z is an `-group ge...

OBJECTIVE To determine the brainstem auditory evoked response (BAER) abnormalities and their reversibility in neonates with birth asphyxia. DESIGN Prospective case control study. SETTING Tertiary care teaching hospital. METHODS 30 term Neonates with 5-min Apgar < 6 and hypoxic ischemic encephalopathy (HIE) underwent BAER testing with follow up at 3 months. An equal number of normal term n...

In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...

We introduce the notions of proto-complete, complete, complete⁎ and strong-complete objects in pointed categories. show under mild conditions on a exact protomodular category that every proto-complete (respectively complete) object is product an abelian object. This together with observation trivial group only complete recovers theorem Baer classifying groups. In addition we generalize several ...