Intersection graphs of subgroups of finite groups

Rulin Shen

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 4, page 945-950
  • ISSN: 0011-4642

Abstract

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In this paper we classify finite groups with disconnected intersection graphs of subgroups. This solves a problem posed by Csákány and Pollák.

How to cite

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Shen, Rulin. "Intersection graphs of subgroups of finite groups." Czechoslovak Mathematical Journal 60.4 (2010): 945-950. <http://eudml.org/doc/196511>.

@article{Shen2010,
abstract = {In this paper we classify finite groups with disconnected intersection graphs of subgroups. This solves a problem posed by Csákány and Pollák.},
author = {Shen, Rulin},
journal = {Czechoslovak Mathematical Journal},
keywords = {intersection graphs; finite groups; subgroups; intersection graphs of subgroups; finite groups; simple groups of Lie type; sporadic simple groups; disconnected graphs},
language = {eng},
number = {4},
pages = {945-950},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Intersection graphs of subgroups of finite groups},
url = {http://eudml.org/doc/196511},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Shen, Rulin
TI - Intersection graphs of subgroups of finite groups
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 945
EP - 950
AB - In this paper we classify finite groups with disconnected intersection graphs of subgroups. This solves a problem posed by Csákány and Pollák.
LA - eng
KW - intersection graphs; finite groups; subgroups; intersection graphs of subgroups; finite groups; simple groups of Lie type; sporadic simple groups; disconnected graphs
UR - http://eudml.org/doc/196511
ER -

References

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  2. Bosák, J., The graphs of semigroups, Theory Graphs Appl., Proc. Symp. Smolenice 1963 (1964), 119-125. (1964) MR0173718
  3. Carter, R., Simple Groups of Lie Type, Wiley London (1972). (1972) Zbl0248.20015MR0407163
  4. Chakrabarty, I., Ghosh, S., Mukherjee, T. K., Sen, M. K., 10.1016/j.endm.2005.06.104, Electronic Notes in Discrete Mathematics 23 (2005), 23-32. (2005) Zbl1193.05086MR2303891DOI10.1016/j.endm.2005.06.104
  5. Csákéany, B., Pollák, G., The graph of subgroups of a finite group, Czechoslovak Math. J. 19 (1969), 241-247. (1969) MR0249328
  6. Kondrat'ev, A. S., 10.1070/SM1990v067n01ABEH001363, Math. USSR Sb. 67 (1989), 235-247. (1989) Zbl0691.20013MR1015040DOI10.1070/SM1990v067n01ABEH001363
  7. Robinson, D. J. S., A Course in the Theory of Groups, Springer New York-Heidelberg-Berlin (1982). (1982) Zbl0483.20001MR0648604
  8. Williams, J. S., 10.1016/0021-8693(81)90218-0, J. Algebra 69 (1981), 487-513. (1981) Zbl0471.20013MR0617092DOI10.1016/0021-8693(81)90218-0
  9. Zelinka, B., Intersection graphs of finite abelian groups, Czech. Math. J. 25 (1975), 171-174. (1975) Zbl0311.05119MR0372075

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