Abstract
The properties of even-order doubly primary subgroups are used to characterize the Ree-type groups as well as certain other finite simple groups.
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Literature cited
Z. Janko and J. G. Thompson, “On a class of finite groups of Ree,” J. Algebra,4, No. 2, 274–292 (1966).
R. Ree, “A family of simple groups associated with the simple Lie algebra of type (G2),” J. Amer. Math. Soc.,83, No. 3, 432–462 (1961).
H. N. Ward, “On Ree's series of simple groups,” Trans. Amer. Math. Soc.,121, No. 1, 62–89 (1966).
J. H. Walter, “The characterization of finite groups with Abelian Sylow 2-subgroups,” Ann. Math.,89, No. 3, 405–514 (1969).
M. Suzuki, “On a finite group with a partition,” Arch. Math.,12, No. 4, 241–254 (1961).
V. D. Mazurov, “Finite simple groups with cyclic intersections of Sylow 2-subgroups,” Algebra i Logika,10, No. 2, 188–198 (1971).
M. Suzuki, “Finite groups of even order in which Sylow 2-subgroups are independent,” Ann. Math.,80, No. 1, 58–77 (1964).
M. Suzuki, “A characterization of the simple groups PSL(2, q),” J. Math. Soc. Japan,20, Nos. 1–2, 342–349 (1968).
V. A. Belonogov, “Characterization of certain finite simple groups by doubly primary subgroups,” Algebra i Logika,10, No. 6, 603–619 (1971).
D. Gorenstein and J. H. Walter, “The characterization of finite groups with dinedral Sylow 2-sub-groups,” (Part I), J. Algebra,2, 85–151; (1965).
D. Gorenstein and J. H. Walter, “The characterization of finite groups with dinedral Sylow 2-sub-groups,” (Part II), J. Algebra,2, 218–270 (1965).
D. Gorenstein and J. H. Walter, “The characterization of finite groups with dinedral Sylow 2-sub-groups,” (Part III), J. Algebra,2, 354–393 (1965).
W. J. Wang, “On finite groups whose 2-Sylow subgroups have cyclic subgroups of index 2,” J. Ausstralian Math. Soc.,4, No. 1, 90–112 (1964).
E. Shult, “On the fusion of an involution in its centralizers,” Not. Amer-Math. Soc.,17, No. 3, 548 (1970).
A. G. Kurosh, The Theory of Groups, Chelsea (1955).
R. Carter, “Simple groups and simple Lie algebras,” J. London Math. Soc.,40, 193–240 (1965).
M. Suzuki, “On a class of doubly transitive groups,” Ann. Math.,75, No. 1, 105–145 (1962).
Z. Janko, “A new finite simple group with Abelian Sylow 2-subgroups and its characterization,” J. Algebra,3, No. 2, 147–186 (1966).
J. Schur, “Untersuchungen über die Darstellung der endlischen Gruppen durch gebrochene lineare Substitutionen,” J. Reine und Angew. Math.,132, No. 2, 85–137 (1907).
H. N. Ward, “On triviality of primary parts of the Schur multiplier,” J. Algebra,10, No. 3, 377–382 (1968).
J. L. Alperin and D. Gorenstein, “The multiplicators of certain simple groups,” Proc. Amer. Math. Soc.,17, No. 2, 515–519 (1966).
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Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 317–324, February, 1973.
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Belonogov, V.A. Characterization of Ree-type groups by doubly primary subgroups. Mathematical Notes of the Academy of Sciences of the USSR 13, 191–195 (1973). https://doi.org/10.1007/BF01094242
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DOI: https://doi.org/10.1007/BF01094242