International Journal of Contemporary Mathematical Sciences, Year (2007-3)

#### Title : On the order of Schur Multipliers of Finite Abelian p-Groups ( On the order of Schur Multipliers of Finite Abelian p-Groups )

Authors: Behrooz Mashayekhy Fard , , ,

Citation: BibTeX | EndNote

#### Abstract

Let $G$ be a finite $p$-group of order $p^{n}$ with $|M(G)|=p^{\\\\frac{n(n-1)}{2}-t},$ where $M(G)$ is the Schur multiplier of $G$. Ya.G. Berkovich, X. Zhou, and G. Ellis have determined the structure of $G$ when $t=0,1,2,3$. In this paper, we are going to find some structures for an abelian $p$-group $G$ with conditions on the exponents of $G, M(G),$ and $S_2M(G)$, where $S_2M(G)$ is the metabelian multiplier of $G$.

Let $G$ be a finite $p$-group of order $p^{n}$ with $|M(G)|=p^{\\\\frac{n(n-1)}{2}-t},$ where $M(G)$ is the Schur multiplier of $G$. Ya.G. Berkovich, X. Zhou, and G. Ellis have determined the structure of $G$ when $t=0,1,2,3$. In this paper, we are going to find some structures for an abelian $p$-group $G$ with conditions on the exponents of $G, M(G),$ and $S_2M(G)$, where $S_2M(G)$ is the metabelian multiplier of $G$.

#### Keywords

, Schur multiplier, Abelian $p$- group.
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@article{paperid:1004479,
author = {Mashayekhy Fard, Behrooz and , and , },
title = {On the order of Schur Multipliers of Finite Abelian p-Groups},
journal = {International Journal of Contemporary Mathematical Sciences},
year = {2007},
month = {March},
issn = {1312-7586},
keywords = {Schur multiplier; Abelian $p$- group.},
}