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Original Articles

Classification of Finite Groups with Toroidal or Projective-Planar Permutability Graphs

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Pages 3705-3726 | Received 02 Apr 2014, Published online: 19 May 2016

REFERENCES

  • Abdollahi, A., Akbary, S., Maimani, H. R. (2006). Non-commuting graph of a group. J. Algebra 298(2):468–492.
  • Archdeacon, D. (2009). Open problems. In: Topics in Topological Graph Theory. Encyclopedia Math. Appl., Vol. 128. Cambridge: Cambridge Univ. Press, pp. 313–336.
  • Aschbacher, M. (1993). Simple connectivity of p-group complexes. Israel J. Math. 82(1–3):1–43.
  • Atlas of Finite Group Representations, http://brauer.maths.qmul.ac.uk/Atlas/(version 2), accessed 13 February 2015.
  • Gillio Berta Mauri, A., Verardi, L. (1995). Finite groups and subgroup-permutability. Ann. Mat. Pura Appl. 169(1):251–268.
  • Bianchi, M., Gillio, A., Verardi, L. (2001). Subgroup-permutability and affine planes. Geometriae Dedicata 85(1–3):147–155.
  • Bohanon, J. P., Reid, L. (2006). Finite groups with planar subgroup lattices. J. Algebraic Combin. 23(3):207–223.
  • Burnside, W. (1955). Theory of Groups of Finite Order. Cambridge: Dover Publications.
  • Cameron, P. J., Ghosh, S. (2011). The power graph of a finite group. Discrete Math. 311(13):1220–1222.
  • Cole, F. N., Glover, J. W. (1893). On groups whose orders are products of three prime factors. American Journal of Mathematics 15(3):191–220.
  • Gagarin, A., Myrvold, W., Chambers, J. (2009). The obstructions for toroidal graphs with no K3, 3's. Discrete Math. 309(11):3625–3631.
  • Gillio, A., Verardi, L. (1996). On finite groups with a reducible permutability-graph. Ann. Mat. Pura Appl. 171(1):275–291.
  • Glover, H. H., Huneke, J. P., Wang, C. S. (1979). 103 graphs that are irreducible for the projective plane. J. Combin. Theory Ser. B 27(3):332–370.
  • Gorenstein, D. (1968). Finite Groups. New York: Harper and Row.
  • Chiang-Hsieh, H.-J. (2008). Classification of rings with projective zero-divisor graphs. J. Algebra 319(7):2789–2802.
  • Kocay, W., Kreher, D. (2005). Graphs, Algorithms, and Optimization. Boca Raton: CRC Press.
  • Lin, H. L. (1974). On groups of order p2q, p2q2. Tamkang J. Math. 5:167–190.
  • Maimani, H. R., Wickham, C., Yassemi, S. (2012). Rings whose total graphs have genus at most one. Rocky Mountain J. Math. 42(5):1551–1560.
  • Neufeld, E., Myrvold, W. (1997). Practical toroidality testing. In: Proc. 8th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 574–580.
  • Rajkumar, R., Devi, P. (2014). Planarity of permutability graphs of subgroups of groups. J. Algebra Appl. 13(3): Article No. 1350112 (15 pages).
  • Rajkumar, R., Devi, P. (2015). On permutability graphs of subgroups of groups. Discrete Math. Algorithm. Appl. 7(2): Article No. 1550012 (11 pages). doi:10.1142/S1793830915500123
  • Scott, W. R. (1964). Group Theory. New York: Dover.
  • Thompson, J. G. (1968). Non-solvable finite groups all of whose local subgroups are solvable I. Bull. Amer. Math. Soc. 74(3):383–437.
  • Wang, H.-J. (2006). Zero-divisor graphs of genus one. J. Algebra 304(2):666–678.
  • White, A. T. (1973). Graphs, Groups and Surfaces. North-Holland Mathematics Studies, Vol. 8. New York: American Elsevier Publishing Co. Inc.
  • Williams, J. S. (1981). Prime graph components of finite groups. J. Algebra 69(2):487–513.

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