Communications in Algebra, ( ISI ), Year (2005-3)

#### Title : ON THE ORDER OF NILPOTENT MULTIPLIERS OF FINITE p-GROUPS ( On the order of nilpotent multipliers of finite p-groups )

Authors: Behrooz Mashayekhy Fard , - - ,

Citation: BibTeX | EndNote

#### Abstract

Let $G$ be a finite $p$-group of order $p^n$. YA. G. Berkovich (Journal of Algebra {\\\\bf 144}, 269-272 (1991)) proved that $G$ is elementary abelian $p$-group if and only if the order of its Schur multiplier, $M(G)$, is at the maximum case. In this paper, first we find the upper bound $p^{\\\\chi_{c+1}{(n)}}$ for the order the $c$-nilpotent multiplier of $G$, $M^{(c)}(G)$, where $\\\\chi_{c+1}{(i)}$ is the number of basic commutators of weight $c+1$ on $i$ letters. Second, we obtain the structure of $G$, in abelian case, where $|M^{(c)}(G)|=p^{\\\\chi_{c+1}{(n-t)}}$, for all $0\\\\leq t\\\\leq n-1$. Finally, by putting a condition on the kernel of the left natural map of the generalized Stallings-Stammbach five term exact sequence, we show that an arbitrary finite $p$-group with the $c$-nilpotent multiplier of maximum order is an elementary abelian $p$-group.

#### Keywords

, Nilpotent multipliers, finite $p$-group, elementary abelian $p$-group.
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@article{paperid:202027,
author = {Mashayekhy Fard, Behrooz and -, -},
title = {ON THE ORDER OF NILPOTENT MULTIPLIERS OF FINITE p-GROUPS},
journal = {Communications in Algebra},
year = {2005},
month = {March},
issn = {0092-7872},
keywords = {Nilpotent multipliers; finite $p$-group; elementary abelian $p$-group.},
}

%0 Journal Article
%T ON THE ORDER OF NILPOTENT MULTIPLIERS OF FINITE p-GROUPS
%A Mashayekhy Fard, Behrooz
%A -, -
%J Communications in Algebra
%@ 0092-7872
%D 2005