Group Theory
Characterizing finite p-groups by their Schur multipliers
Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 867-870.

It has been proved in J.A. Green (1956) [5] for every p-group of order $pn$, $|M(G)|=p12n(n−1)−t(G)$, where $t(G)⩾0$. In Ya.G. Berkovich (1991) [1], G. Ellis (1999) [4], and X. Zhou (1994) [14], the structure of G has been characterized for $t(G)=0,1,2,3$ by several authors. Also in A.R. Salemkar et al. (2007) [12], the structure of G characterized when $t(G)=4$ and $Z(G)$ is elementary abelian, but there are some missing points in classifying the structure of these groups. This paper is devoted to classify the structure of G when $t(G)=4$ without any condition and with a short and quite different way to that of Ya.G. Berkovich (1991) [1], G. Ellis (1999) [4], A.R. Salemkar et al. (2007) [12], and X. Zhou (1994) [14].

Il est montré dans J.A. Green (1956) [5] que pour tout p-groupe dʼordre $pn$ on a $|M(G)|=pn(n−1)2−t(G)$$t(G)⩾0$. Dans Ya.G. Berkovich (1991) [1], G. Ellis (1999) [4], et X. Zhou (1994) [14] la structure de G a été classifiée par plusieurs auteurs pour $t(G)=0,1,2,3$. Également, dans A.R. Salemkar et al. (2007) [12] la structure de G est caractérisée lorsque $t(G)=4$ et $Z(G)$ est abelien élémentaire, mais il y a quelques trous dans la classification complète de ces groupes. Cette Note est consacrée à la caractérisation de la structure de G lorsque $t(G)=4$, sans restriction aucune et dʼune manière différente, plus directe que les approches de Ya.G. Berkovich (1991) [1], G. Ellis (1999) [4], A.R. Salemkar et al. (2007) [12], et X. Zhou (1994) [14].

Accepted:
Published online:
DOI: 10.1016/j.crma.2012.10.018

Peyman Niroomand 1

1 School of Mathematics and Computer Science, Damghan University, Damghan, Iran
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Peyman Niroomand. Characterizing finite p-groups by their Schur multipliers. Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 867-870. doi : 10.1016/j.crma.2012.10.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.018/

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