Research Article
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Year 2018, Volume: 24 Issue: 24, 73 - 90, 05.07.2018
https://doi.org/10.24330/ieja.440221

Abstract

References

  • S. Abe, A characterization of some nite simple groups by orders of their solvable subgroups, Hokkaido Math. J., 31(2) (2002), 349-361.
  • S. Abe and N. Iiyori, A generalization of prime graphs of nite groups, Hokkaido Math. J., 29(2) (2000), 391-407.
  • B. Akbari, N. Iiyori and A. R. Moghaddamfar, A new characterization of some simple groups by order and degree pattern of solvable graph, Hokkaido Math. J., 45(3) (2016), 337-363.
  • J. N. Bray, D. F. Holt and C. M. Roney-Dougal, The Maximal Subgroups of the Low-Dimensional Finite Classical Groups, London Mathematical Society Lecture Note Series, 407, Cambridge University Press, Cambridge, 2013.
  • A. A. Buturlakin, Spectra of nite linear and unitary groups, Algebra Logic, 47(2) (2008), 91-99.
  • J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Oxford University Press, Eynsham, 1985.
  • O. H. King, The subgroup structure of nite classical groups in terms of geo- metric con gurations, Surveys in combinatorics, London Math. Soc., Lecture Note Ser., 327, Cambridge Univ. Press, Cambridge, (2005), 29-56.
  • A. V. Vasilev and E. P. Vdovin, An adjacency criterion in the prime graph of a nite simple group, Algebra Logic, 44(6) (2005), 381-406.
  • A. V. Vasilev and E. P. Vdovin, Cocliques of maximal size in the prime graph of a nite simple group, Algebra Logic, 50(4) (2011), 291-322.
  • A. V. Zavarnitsin and V. D. Mazurov, Element orders in coverings of symmet- ric and alternating groups, Algebra Logic, 38(3) (1999), 159-170.
  • K. Zsigmondy, Zur theorie der potenzreste, Monatsh. Math. Phys., 3(1) (1892) 265-284.

ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS

Year 2018, Volume: 24 Issue: 24, 73 - 90, 05.07.2018
https://doi.org/10.24330/ieja.440221

Abstract

The solvable graph of a nite group G, which is denoted by
􀀀s(G), is a simple graph whose vertex set is comprised of the prime divisors
of jGj and two distinct primes p and q are joined by an edge if and
only if there exists a solvable subgroup of G such that its order is divisible
by pq. Let p1 < p2 < < pk be all prime divisors of jGj and let
Ds(G) = (ds(p1); ds(p2); : : : ; ds(pk)), where ds(p) signies the degree of the
vertex p in 􀀀s(G). We will simply call Ds(G) the degree pattern of solvable
graph of G. A nite group H is said to be ODs-characterizable if H = G for
every nite group G such that jGj = jHj and Ds(G) = Ds(H). In this paper,
we study the solvable graph of some subgroups and some extensions of a nite
group. Furthermore, we prove that the linear groups L3(q) with certain properties,
are ODs-characterizable

References

  • S. Abe, A characterization of some nite simple groups by orders of their solvable subgroups, Hokkaido Math. J., 31(2) (2002), 349-361.
  • S. Abe and N. Iiyori, A generalization of prime graphs of nite groups, Hokkaido Math. J., 29(2) (2000), 391-407.
  • B. Akbari, N. Iiyori and A. R. Moghaddamfar, A new characterization of some simple groups by order and degree pattern of solvable graph, Hokkaido Math. J., 45(3) (2016), 337-363.
  • J. N. Bray, D. F. Holt and C. M. Roney-Dougal, The Maximal Subgroups of the Low-Dimensional Finite Classical Groups, London Mathematical Society Lecture Note Series, 407, Cambridge University Press, Cambridge, 2013.
  • A. A. Buturlakin, Spectra of nite linear and unitary groups, Algebra Logic, 47(2) (2008), 91-99.
  • J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Oxford University Press, Eynsham, 1985.
  • O. H. King, The subgroup structure of nite classical groups in terms of geo- metric con gurations, Surveys in combinatorics, London Math. Soc., Lecture Note Ser., 327, Cambridge Univ. Press, Cambridge, (2005), 29-56.
  • A. V. Vasilev and E. P. Vdovin, An adjacency criterion in the prime graph of a nite simple group, Algebra Logic, 44(6) (2005), 381-406.
  • A. V. Vasilev and E. P. Vdovin, Cocliques of maximal size in the prime graph of a nite simple group, Algebra Logic, 50(4) (2011), 291-322.
  • A. V. Zavarnitsin and V. D. Mazurov, Element orders in coverings of symmet- ric and alternating groups, Algebra Logic, 38(3) (1999), 159-170.
  • K. Zsigmondy, Zur theorie der potenzreste, Monatsh. Math. Phys., 3(1) (1892) 265-284.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

B. Akbari This is me

Publication Date July 5, 2018
Published in Issue Year 2018 Volume: 24 Issue: 24

Cite

APA Akbari, B. (2018). ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS. International Electronic Journal of Algebra, 24(24), 73-90. https://doi.org/10.24330/ieja.440221
AMA Akbari B. ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS. IEJA. July 2018;24(24):73-90. doi:10.24330/ieja.440221
Chicago Akbari, B. “ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS”. International Electronic Journal of Algebra 24, no. 24 (July 2018): 73-90. https://doi.org/10.24330/ieja.440221.
EndNote Akbari B (July 1, 2018) ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS. International Electronic Journal of Algebra 24 24 73–90.
IEEE B. Akbari, “ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS”, IEJA, vol. 24, no. 24, pp. 73–90, 2018, doi: 10.24330/ieja.440221.
ISNAD Akbari, B. “ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS”. International Electronic Journal of Algebra 24/24 (July 2018), 73-90. https://doi.org/10.24330/ieja.440221.
JAMA Akbari B. ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS. IEJA. 2018;24:73–90.
MLA Akbari, B. “ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS”. International Electronic Journal of Algebra, vol. 24, no. 24, 2018, pp. 73-90, doi:10.24330/ieja.440221.
Vancouver Akbari B. ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS. IEJA. 2018;24(24):73-90.