| Title:
|
Intersection graphs of subgroups of finite groups (English) |
| Author:
|
Shen, Rulin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
945-950 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we classify finite groups with disconnected intersection graphs of subgroups. This solves a problem posed by Csákány and Pollák. (English) |
| Keyword:
|
intersection graphs |
| Keyword:
|
finite groups |
| Keyword:
|
subgroups |
| MSC:
|
20D06 |
| MSC:
|
20D60 |
| idZBL:
|
Zbl 1208.20022 |
| idMR:
|
MR2738958 |
| . |
| Date available:
|
2010-11-20T13:53:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140795 |
| . |
| Reference:
|
[1] Aschbacher, M.: On the maximal subgroups of the finite classical groups.Invent. Math. 76 (1984), 469-514. Zbl 0537.20023, MR 0746539, 10.1007/BF01388470 |
| Reference:
|
[2] Bosák, J.: The graphs of semigroups.Theory Graphs Appl., Proc. Symp. Smolenice 1963 (1964), 119-125. MR 0173718 |
| Reference:
|
[3] Carter, R.: Simple Groups of Lie Type.Wiley London (1972). Zbl 0248.20015, MR 0407163 |
| Reference:
|
[4] Chakrabarty, I., Ghosh, S., Mukherjee, T. K., Sen, M. K.: Intersection graphs of ideals of rings.Electronic Notes in Discrete Mathematics 23 (2005), 23-32. Zbl 1193.05086, MR 2303891, 10.1016/j.endm.2005.06.104 |
| Reference:
|
[5] Csákéany, B., Pollák, G.: The graph of subgroups of a finite group.Czechoslovak Math. J. 19 (1969), 241-247. MR 0249328 |
| Reference:
|
[6] Kondrat'ev, A. S.: Prime graph components of finite simple groups.Math. USSR Sb. 67 (1989), 235-247. Zbl 0691.20013, MR 1015040, 10.1070/SM1990v067n01ABEH001363 |
| Reference:
|
[7] Robinson, D. J. S.: A Course in the Theory of Groups.Springer New York-Heidelberg-Berlin (1982). Zbl 0483.20001, MR 0648604 |
| Reference:
|
[8] Williams, J. S.: Prime graph components of finite groups.J. Algebra 69 (1981), 487-513. Zbl 0471.20013, MR 0617092, 10.1016/0021-8693(81)90218-0 |
| Reference:
|
[9] Zelinka, B.: Intersection graphs of finite abelian groups.Czech. Math. J. 25 (1975), 171-174. Zbl 0311.05119, MR 0372075 |
| . |
