Czechoslovak Mathematical Journal, first online, pp. 1-7


Breaking points in the poset of conjugacy classes of subgroups of a finite group

Marius Tărnăuceanu

Received October 24, 2018.   Published online June 3, 2019.

Abstract:  We determine the finite groups whose poset of conjugacy classes of subgroups has breaking points. This leads to a new characterization of the generalized quaternion 2-groups. A generalization of this property is also studied.
Keywords:  breaking point; poset of conjugacy classes of subgroups; interval; generalized quaternion 2-group
Classification MSC:  20D30, 20D15, 20E15
DOI:  10.21136/CMJ.2019.0066-18

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References:
[1] S. Breaz, G. Călugăreanu: Abelian groups whose subgroup lattice is the union of two intervals. J. Aust. Math. Soc. 78 (2005), 27-36. DOI 10.1017/s1446788700015548 | MR 2129487 | Zbl 1080.20023
[2] G. Călugăreanu, M. Deaconescu: Breaking points in subgroup lattices. Proc. Conf. Groups St. Andrews 2001 in Oxford. Vol. I (C. M. Campbell et al., eds.). London Mathematical Society Lecture Note Series 304, Cambridge University Press, Cambridge (2003), 59-62. DOI 10.1017/CBO9780511542770.012 | MR 2051518 | Zbl 1062.20028
[3] Y. Chen, G. Chen: A note on a characterization of generalized quaternion 2-groups. C. R., Math., Acad. Sci. Paris 352 (2014), 459-461. DOI 10.1016/j.crma.2014.04.009 | MR 3210124 | Zbl 1303.20019
[4] I. M. Isaacs: Finite Group Theory. Graduate Studies in Mathematics 92, American Mathematical Society, Providence (2008). DOI 10.1090/gsm/092 | MR 2426855 | Zbl 1169.20001
[5] R. Schmidt: Subgroup Lattices of Groups. De Gruyter Expositions in Mathematics 14, Walter de Gruyter, Berlin (1994). DOI 10.1515/9783110868647 | MR 1292462 | Zbl 0843.20003
[6] M. Suzuki: On the lattice of subgroups of finite groups. Trans. Am. Math. Soc. 70 (1951), 345-371. DOI 10.1090/S0002-9947-1951-0039717-3 | MR 0039717 | Zbl 0043.02502
[7] M. Suzuki: Group Theory I. Grundlehren der Mathematischen Wissenschaften 247, Springer, Berlin (1982). MR 0648772 | Zbl 0472.20001
[8] M. Suzuki: Group Theory II. Grundlehren der Mathematischen Wissenschaften 248, Springer, Berlin (1986). MR 0501682 | Zbl 0472.20001
[9] M. Tărnăuceanu: A characterization of generalized quaternion 2-groups. C. R., Math., Acad. Sci. Paris 348 (2010), 731-733. DOI 10.1016/j.crma.2010.06.016 | MR 2671150 | Zbl 1205.20024
[10] M. Tărnăuceanu: Contributions to the Study of Subgroup Lattices. Matrix Rom, Bucharest (2016). MR 3496569 | Zbl 1360.20002

Affiliations:   Marius Tărnăuceanu, Faculty of Mathematics, "Al. I. Cuza" University, Bd. Carol I, nr. 11, 700506, Jasy, Romania, e-mail: tarnauc@uaic.ro


 
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