相关论文: On the Nilpotent Multiplier of a Free Product
In this article, we present an explicit formula for the $c$th nilpotent multiplier (the Baer invariant with respect to the variety of nilpotent groups of class at most $c\geq 1$) of the $n$th nilpotent product of some cyclic groups…
In this paper, we use the theory of simplicial groups to develop the Schur multiplier of a pair of groups $(G,N)$ to the Baer invariant of it, $\mathcal{V}M(G,N)$, with respect to an arbitrary variety $\mathcal{V}$. Moreover, we present…
In this paper, using the topological interpretation of the Baer invariant of a group $G$, $\mathcal{V}M(G)$, with respect to an arbitrary variety $\mathcal{V}$, we extend a result of Burns and Ellis (Math. Z. 226 (1997) 405-428) on the…
In this paper, we present an explicit structure for the Baer invariant of a free nilpotent group (the $n$-th nilpotent product of the infinite cyclic group, $\textbf{Z}\st{n}* \textbf{Z}\st{n}*... \st{n}*\textbf{Z}$) with respect to the…
We present an explicit structure for the Baer invariant of a free $n$th nilpotent group (the $n$th nilpotent product of infinite cyclic groups, $\textbf{Z}\st{n}* \textbf{Z}\st{n}*...\st{n}*\textbf{Z}$) with respect to the variety ${\cal…
This article is devoted to present an explicit formula for the $c$th nilpotent multiplier of nilpotent products of some cyclic groups $G={\bf {Z}}\stackrel{n_1}{*}{\bf {Z}}\stackrel{n_2}{*}...\stackrel{n_{t-1}}{*}{\bf…
The paper is devoted to finding a homomorphic image for the $c$-nilpotent multiplier of the verbal product of a family of groups with respect to a variety ${\mathcal V}$ when ${\mathcal V} \subseteq {\mathcal N}_{c}$ or ${\mathcal…
W.Haebich (Bull. Austral. Math. Soc., 7, 1972, 279-296) presented a formula for the Schur multiplier of a regular product of groups. In this paper first, it is shown that the Baer-invariant of a nilpotent product of groups with respect to…
In this paper we present some inequalities for the order, the exponent, and the number of generators of the c-nilpotent multiplier (the Baer invariant with respect to the variety of nilpotent groups of class at most $c \geq 1$) of a…
In this paper we present some inequalities for the order, the exponent and the number of generators of the $c$-nilpotent multiplier (the Baer invariant with respect to the variety of nilpotent groups of class at most $c \geq 1$) of a finite…
In this paper, first we obtain an explicit formula for an outer commutator multiplier of nilpotent products of cyclic groups with respect to the variety $[\mathfrak{N}_{c_1},\mathfrak{N}_{c_2}]$, $\mathfrak{N}_{c}M(\mathbb{Z}\st{n}*…
There has been a great importance in understanding the nilpotent multipliers of finite groups in recent past. Let a group $G$ be presented as the quotient of a free group $F$ by a normal subgroup $R$. Given a positive integer $c$, the…
The first author, in 2001, presented a structure for the Baer-invariant of a nilpotent product of cyclic groups with respect to the variety of nilpotent groups. In this paper, using the above structure, we prove the existence of an ${\cal…
In this paper, we are going to look at the $c$-nilpotent multiplier of a group $G$, ${\cal N}_cM(G)$, as a functor from the category of all groups, ${\cal G}roup$, to the category of all abelian groups, ${\cal A}b$, and focusing on some…
In this article we show that if ${\cal V}$ is the variety of polynilpotent groups of class row $(c_1,c_2,...,c_s),\ {\mathcal N}_{c_1,c_2,...,c_s}$, and $G\cong{\bf {Z}}_{p^{\alpha_1}}\stackrel{n}{*}{\bf…
In this paper, we present an explicit formula for the Baer invariant of a finitely generated abelian group with respect to the variety of polynilpotent groups of class row $(c_1,...,c_t)$, ${\cal N}_{c_1,...,c_t}$. In particular, one can…
Let G be the free product of groups A and B with commuting subgroups H \leqslant A and K \leqslant B, and let C be the class of all finite groups or the class of all finite p-groups. We derive the description of all C-separable cyclic…
W. Haebich (1977, Journal of Algebra {\bf 44}, 420-433) presented some formulas for the Schur multiplier of a semidirect product and also a verbal wreath product of two groups. The author (1997, Indag. Math., (N.S.), {\bf 8}({\bf 4}),…
In this paper, we develop the theory of Baer invariants for triples of groups. First, we focus on the general properties of the Baer invariant of triples. Second, we prove that the Baer invariant of a triple preserves direct limits of…
In this paper, we determine the behavior of the $c$-nilpotent multiplier of Lie algebras with respect to the direct sums. Then we give some results on the $c$-capability of the direct sum of finite dimensional Lie algebras.