Advertisement

Algebra and Logic

, Volume 39, Issue 1, pp 42–49 | Cite as

Infinite groups with Abelian centralizers of involutions

  • V. D. Mazurov
Article

Abstract

The article contains two characterizations of projective linear groups PGL2(P) over a locally finite field P of characteristic 2: the first is defined in terms of permutation groups, and the second, in terms of a structure of involution centralizers. One of the two is used to prove the existence of infinite groups which are recognizable by the set of their element orders.

Keywords

Finite Group Finite Field Multiplicative Group Element Order Transitive Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Zassenhaus, “Kennzeichnung endlicher linearen Gruppen als Permutationsgruppen,”Abh. Math. Sem. Univ. Hamburg,11, 17–40 (1936).CrossRefGoogle Scholar
  2. 2.
    B. Huppert and N. Blackburn,Finite Groups. III, Springer, Berlin (1982).zbMATHGoogle Scholar
  3. 3.
    M. Suzuki, “On characterizations of linear groups. I,”Trans. Am. Math. Soc.,92, 191–219 (1959).CrossRefGoogle Scholar
  4. 4.
    R. Brauer, M. Suzuki, and G. E. Wall, “A characterization of the one-dimensional unimodular projective groups over finite fields,”Ill. J. Math.,2, No. 3, 718–742 (1958).MathSciNetGoogle Scholar
  5. 5.
    D. Goldshmidt, “Elements of order two in finite groups,”Delta (Waukesha),4, 45–58 (1974/75).MathSciNetGoogle Scholar
  6. 6.
    H. Deng and W. Shi, “The characterization of Ree groups2 F 4(q) by their element orders,”J. Alg.,217, No. 1, 180–187 (1999).zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    V. D. Mazurov, “2-Transitive permutation groups,”Sib. Mat. Zh.,31, No. 4, 102–104 (1990).MathSciNetGoogle Scholar
  8. 8.
    M. Suzuki, “On a class of doubly transitive groups,”Ann. Math., II. Ser.,75, No. 1, 105–145 (1962).Google Scholar
  9. 9.
    M. Suzuki, “On a class of doubly transitive groups, II”Ann. Math., II. Ser.,80, No. 1, 58–77 (1964).Google Scholar
  10. 10.
    D. Gorenstein,Finite Groups, Chelsea, New York (1980).Google Scholar
  11. 11.
    A. Kh. Zhurtov and V. D. Mazurov, “On recognition of finite simple groupsL 2(2m) in the class of all groups,”Sib. Mat. Zh.,40, No. 1, 75–78 (1999).zbMATHMathSciNetGoogle Scholar
  12. 12.
    The Kourovka Notebook, Institute of Mathematics SO RAN, Novosibirsk (1999).Google Scholar
  13. 13.
    A. I. Sozutov and N. M. Suchkov, “On some doubly transitive groups,” Preprint, Inst. Comp. Math. SB RAS, Krasnoyarsk (1998).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • V. D. Mazurov

There are no affiliations available

Personalised recommendations