Comptes Rendus
Group Theory
Characterizing finite p-groups by their Schur multipliers
[Caractérisation des p-groupes finis par leurs multiplicateurs de Schur]
Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 867-870.

Il est montré dans J.A. Green (1956) [5] que pour tout p-groupe dʼordre pn on a |M(G)|=pn(n1)2t(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].

It has been proved in J.A. Green (1956) [5] for every p-group of order pn, |M(G)|=p12n(n1)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].

Reçu le :
Accepté le :
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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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[12] A.R. Salemkar; M.R.R. Moghaddam; M. Davarpanah; F. Saeedi A remark on the Schur multiplier of p-groups, Comm. Algebra, Volume 35 (2007), pp. 1215-1221

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