相关论文: The Higher Schur-Multiplicator of Certain Classes …

In this paper we obtain an explicit formula for the higher Schur-multiplicator of an arbitrary finite abelian group with respect to the variety of nilpotent groups of class at most $c\geq 1$ .

We describe an algorithm for computing successive quotients of the Schur multiplier $M(G)$ for a group $G$ given by an invariant finite $L$-presentation. As application, we investigate the Schur multipliers of various self-similar groups…

The paper is devoted to obtain an upper bound for the Schur multiplier of nilpotent Lie algebras of maximal class. It improves the later upper bounds on the Schur multiplier of such Lie algebras.

Let $p$ be an odd prime. We describe a method to compute the Schur multiplier of finite $p$-groups $G$ of nilpotency class $2$ such that $G/[G,G]$ is isomorphic to direct product of copies of $\mathbb{Z}_{p^s}$ for $s \in \mathbb{N}$,…

A longstanding problem attributed to I. Schur says that for a finite group $G$, the exponent of the second homology group $H_2(G, \mathbb{Z})$ divides the exponent of $G$. In this paper, we prove this conjecture for finite nilpotent groups…

An explicit formula for the Schur multiplier of the group of unitriangular matrices over products of cyclic rings $\ZZ/m\ZZ$ and $\ZZ$ is derived. We use it to provide presentations of the corresponding covering groups and touch upon the…

From [Problem 1729, Groups of prime power order, Vol. 3], Berkovich et al. asked to obtain the Schur multiplier and the representation of a group $G$, when $G$ is a special $p$-group minimally generated by $d$ elements and…

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 1998, G. Ellis defined the Schur multiplier of a pair $(G,N)$ of groups and mentioned that this notion is a useful tool for studying pairs of groups. In this paper, we characterize the structure of a pair of finite $p$-groups $(G,N)$ in…

In this article, we study the Schur mutiplier of the discrete as well as the finite Heisenberg groups and their t-variants. We describe the representation groups of these Heisenberg groups and through these give a construction of their…

We consider the Schur multipliers of finite dimensional nilpotent Lie algebras. If the algebra has dimension greater than one, then the Schur multiplier is non-zero. We give a direct proof of an upper bound for the dimension of the Schur…

Let $G$ be a central product of two groups $H$ and $K$. We study second cohomology group of $G$, having coefficients in a divisible abelian group $D$ with trivial $G$-action, in terms of the second cohomology groups of certain quotients of…

In this note, we give short proofs of the well-known results that the exponent of the Schur multiplier $\M$ divides the exponent of $\G$ for finite $\p$-groups of maximal class and potent $\p$-groups. Moreover, we prove the same for a…

M.R.Jones and J.Wiegold in [3] have shown that if $G$ is a finite group with a subgroup $H$ of finite index $n$, then the $n$-th power of Schur multiplier of $G$, $M(G)^n$, is isomorphic to a subgroup of $M(H)$. In this paper we prove a…

In 1956, Green provided a bound on the order of the Schur multiplier of $p$-groups. This bound, given as a function of the order of the group, is the best possible. Since then, the bound has been refined numerous times by adding other…

We give a bound on the order of the Schur multiplier of $p$-groups refining earlier bounds. As an application we complete the classification of groups having Schur multiplier of maximum order. Finally we prove that the order of the Schur…

A group G is called special p-group of rank k if the commutator subgroup [G,G] and centre Z(G) are equal, which is elementary abelian p-group of rank k and G/[G,G] is also elementary abelian p-group. In this article we determine the Schur…

Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $\exp(G)$ and let $m=\lfloor\log_pk\rfloor$. We show that $\exp(M^{(c)}(G))$ divides $\exp(G)p^{m(k-1)}$, for all $c\geq1$, where $M^{(c)}(G)$ denotes the c-nilpotent…

In this paper, we find an upper bound for the exponent of the Schur multiplier of a pair $(G,N)$ of finite $p$-groups, when $N$ admits a complement in $G$. As a consequence, we show that the exponent of the Schur multiplier of a pair…

We obtain bounds for the size of the Schur multiplier of finite $p$-groups and finite groups, which improve all existing bounds. Moreover, we obtain bounds for the size of the second cohomology group $H^2(G,\mathbb{Z}/p\mathbb{Z})$ of a…