Comptes Rendus
no. 6
Algebra/Group theory
A note on a characterization of generalized quaternion 2-groups
[Caractérisation des 2-groupes de quaternions généralisés]

Présenté par : the Editorial Board

Yanheng Chen1, 2 ; Guiyun Chen1
1 School of Mathematics and Statistics, Southwest University, Chongqing 400715, PR China
2 School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, PR China
Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 459-461.

Répondant à une question de M. Tărnăceanu (2010) [5], nous montrons que les 2-groupes de quaternions généralisés sont les seuls groupes finis non cycliques dont le treillis des classes de conjugaison de sous-groupes cycliques admet un point clivant.

In this note, we answer an open problem posed in M. Tărnăceanu (2010) [5], and obtain that the generalized quaternion 2-groups are the unique finite noncyclic groups whose posets of conjugacy classes of cyclic subgroups have breaking points.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.04.009
Yanheng Chen 1, 2 ; Guiyun Chen 1

1 School of Mathematics and Statistics, Southwest University, Chongqing 400715, PR China
2 School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, PR China 
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Yanheng Chen; Guiyun Chen. A note on a characterization of generalized quaternion 2-groups. Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 459-461. doi : 10.1016/j.crma.2014.04.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.04.009/

[1] G.G. Călugăreanu; M. Deaconescu Breaking points in subgroup lattices (C.M. Campbell; E.F. Robertson; G.C. Smith, eds.), Proceedings of Groups St. Andrews 2001 in Oxford, vol. 1, Cambridge University Press, Cambridge, UK, 2003, pp. 59-62

[2] B. Fein; W.M. Kantor; M. Schacher Relative Brauer groups. II, J. Reine Angew. Math., Volume 328 (1980), pp. 39-57

[3] B. Huppert Endliche Gruppen, I, Springer-Verlag, Berlin, Heidelberg, New York, 1967

[4] M. Tărnăuceanu Groups Determined by Posets of Subgroups, Ed. Matrix Rom, Bucuresti, Romania, 2006

[5] M. Tărnăuceanu A characterization of generalized quaternion 2-groups, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010), pp. 731-733

Cité par Sources :

☆ This work was supported by National Natural Science Foundation of China (Grant Nos. 11271301, 11001226), and the Fundamental Research Funds for the Central Universities.

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