[Caractérisation des 2-groupes de quaternions généralisés]
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.
Accepté le :
Publié le :
@article{CRMATH_2014__352_6_459_0,
author = {Chen, Yanheng and Chen, Guiyun},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.04.009/}
}
TY - JOUR AU - Chen, Yanheng AU - Chen, Guiyun 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2014.04.009/ DO - 10.1016/j.crma.2014.04.009 LA - en ID - CRMATH_2014__352_6_459_0 ER -
%0 Journal Article %A Chen, Yanheng %A Chen, Guiyun %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 %U http://www.numdam.org/articles/10.1016/j.crma.2014.04.009/ %R 10.1016/j.crma.2014.04.009 %G en %F CRMATH_2014__352_6_459_0
Chen, Yanheng; Chen, Guiyun. A note on a characterization of generalized quaternion 2-groups. Comptes Rendus. Mathématique, Tome 352 (2014) no. 6, pp. 459-461. doi : 10.1016/j.crma.2014.04.009. http://www.numdam.org/articles/10.1016/j.crma.2014.04.009/
[1] Breaking points in subgroup lattices (Campbell, C.M.; Robertson, E.F.; Smith, G.C., eds.), Proceedings of Groups St. Andrews 2001 in Oxford, vol. 1, Cambridge University Press, Cambridge, UK, 2003, pp. 59-62
[2] Relative Brauer groups. II, J. Reine Angew. Math., Volume 328 (1980), pp. 39-57
[3] Endliche Gruppen, I, Springer-Verlag, Berlin, Heidelberg, New York, 1967
[4] Groups Determined by Posets of Subgroups, Ed. Matrix Rom, Bucuresti, Romania, 2006
[5] 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.
