| Title:
|
Breaking points in the poset of conjugacy classes of subgroups of a finite group (English) |
| Author:
|
Tărnăuceanu, Marius |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
1081-1087 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
breaking point |
| Keyword:
|
poset of conjugacy classes of subgroups |
| Keyword:
|
interval |
| Keyword:
|
generalized quaternion $2$-group |
| MSC:
|
20D15 |
| MSC:
|
20D30 |
| MSC:
|
20E15 |
| idZBL:
|
07144877 |
| idMR:
|
MR4039622 |
| DOI:
|
10.21136/CMJ.2019.0066-18 |
| . |
| Date available:
|
2019-11-28T08:51:55Z |
| Last updated:
|
2022-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147916 |
| . |
| Reference:
|
[1] Breaz, S., Călugăreanu, G.: Abelian groups whose subgroup lattice is the union of two intervals.J. Aust. Math. Soc. 78 (2005), 27-36. Zbl 1080.20023, MR 2129487, 10.1017/s1446788700015548 |
| Reference:
|
[2] Călugăreanu, G., Deaconescu, M.: Breaking points in subgroup lattices.Proc. Conf. Groups St. Andrews 2001 in Oxford. Vol. I C. M. Campbell et al. London Mathematical Society Lecture Note Series 304, Cambridge University Press, Cambridge (2003), 59-62. Zbl 1062.20028, MR 2051518, 10.1017/CBO9780511542770.012 |
| Reference:
|
[3] Chen, Y., Chen, G.: A note on a characterization of generalized quaternion 2-groups.C. R., Math., Acad. Sci. Paris 352 (2014), 459-461. Zbl 1303.20019, MR 3210124, 10.1016/j.crma.2014.04.009 |
| Reference:
|
[4] Isaacs, I. M.: Finite Group Theory.Graduate Studies in Mathematics 92, American Mathematical Society, Providence (2008). Zbl 1169.20001, MR 2426855, 10.1090/gsm/092 |
| Reference:
|
[5] Schmidt, R.: Subgroup Lattices of Groups.De Gruyter Expositions in Mathematics 14, Walter de Gruyter, Berlin (1994). Zbl 0843.20003, MR 1292462, 10.1515/9783110868647 |
| Reference:
|
[6] Suzuki, M.: On the lattice of subgroups of finite groups.Trans. Am. Math. Soc. 70 (1951), 345-371. Zbl 0043.02502, MR 0039717, 10.1090/S0002-9947-1951-0039717-3 |
| Reference:
|
[7] Suzuki, M.: Group Theory I.Grundlehren der Mathematischen Wissenschaften 247, Springer, Berlin (1982). Zbl 0472.20001, MR 0648772, 10.1007/978-3-642-61804-8 |
| Reference:
|
[8] Suzuki, M.: Group Theory II.Grundlehren der Mathematischen Wissenschaften 248, Springer, Berlin (1986). Zbl 0472.20001, MR 0501682, 10.1007/978-3-642-86885-6_3 |
| Reference:
|
[9] Tărnăuceanu, M.: A characterization of generalized quaternion 2-groups.C. R., Math., Acad. Sci. Paris 348 (2010), 731-733. Zbl 1205.20024, MR 2671150, 10.1016/j.crma.2010.06.016 |
| Reference:
|
[10] Tărnăuceanu, M.: Contributions to the Study of Subgroup Lattices.Matrix Rom, Bucharest (2016). Zbl 1360.20002, MR 3496569 |
| . |
