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A characterization of a finite simple Hall-Janko group

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Abstract

A finite simple Hall-Janko group in the class of simple groups is characterized by the structure of the centralizer of a central involution.

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Literature cited

  1. Z. Janko, “A new finite simple group with Abelian 2-Sylow subgroups and its characterization,” J. Algebra,3, 147–186 (1966).

    Google Scholar 

  2. Z. Janko and J. Thompson, “On a class of finite simple groups of Ree,” J. Algebra,4, 274–292 (1966).

    Google Scholar 

  3. H. Ward, “On Ree's series of simple groups,” Trans. Amer. Math. Soc.,121, 62–89 (1966).

    Google Scholar 

  4. Z. Janko, “Some new simple groups of finite order,” Symp. Math. I, London and New York (1968), pp. 25–69.

  5. D. Gorenstein and K. Harada, “A characterization of Janko's two new simple groups,” J. Fac. Sci. Univ. Tokyo,16, 331–406 (1970).

    Google Scholar 

  6. D. Gorenstein and K. Harada, “Finite groups whose Sylow 2-subgroups are the direct product of two dihedral groups,” Ann. of Math.,95, 1–54 (1972).

    Google Scholar 

  7. J. Walter, “The characterization of finite groups with Abelian Sylow 2-subgroups,” Ann. of Math.,89, 405–514 (1969).

    Google Scholar 

  8. K. Harada, “Finite simple groups with short chains of subgroups,” J. Math. Soc. Japan,20, 655–672 (1968).

    Google Scholar 

  9. M. Hall, The Theory of Groups, Macmillan, New York (1959).

    Google Scholar 

  10. A. MacWilliams, “On 2-groups with no normal Abelian subgroups of rank 3 and their occurrence as Sylow 2-subgroups of finite groups,” Trans. Amer. Math. Soc.,150, 345–408 (1970).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 535–542, October, 1973.

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Il'inykh, A.P. A characterization of a finite simple Hall-Janko group. Mathematical Notes of the Academy of Sciences of the USSR 14, 866–869 (1973). https://doi.org/10.1007/BF01108815

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  • DOI: https://doi.org/10.1007/BF01108815

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