A note on a characterization of generalized quaternion 2-groups

Yanheng Chen; Guiyun Chen

doi:10.1016/j.crma.2014.04.009

Algebra/Group theory

A note on a characterization of generalized quaternion 2-groups

Presented by: the Editorial Board

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

Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 459-461.

Abstract
Résumé

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.

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.

Received: 2013-12-06
Accepted: 2014-04-23
Published online: 2014-05-10

DOI: 10.1016/j.crma.2014.04.009

Author's affiliations:

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

@article{CRMATH_2014__352_6_459_0,
     author = {Yanheng Chen and Guiyun Chen},
     title = {A note on a characterization of generalized quaternion 2-groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {459--461},
     publisher = {Elsevier},
     volume = {352},
     number = {6},
     year = {2014},
     doi = {10.1016/j.crma.2014.04.009},
     language = {en},
}

TY  - JOUR
AU  - Yanheng Chen
AU  - Guiyun Chen
TI  - A note on a characterization of generalized quaternion 2-groups
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 459
EP  - 461
VL  - 352
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2014.04.009
LA  - en
ID  - CRMATH_2014__352_6_459_0
ER  -

%0 Journal Article
%A Yanheng Chen
%A Guiyun Chen
%T A note on a characterization of generalized quaternion 2-groups
%J Comptes Rendus. Mathématique
%D 2014
%P 459-461
%V 352
%N 6
%I Elsevier
%R 10.1016/j.crma.2014.04.009
%G en
%F CRMATH_2014__352_6_459_0

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/

References
Cited by

[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

Cited by 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.

Comments - Policy