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References
Alperin, J., andD. Gorenstein: The multiplicators of certain simple groups. Proc. Am. Math. Soc.17, 515–519 (1966).
Artin, E.: The orders of the linear groups. Comm. Pure and Applied Math.8, 355–366 (1955).
Blackburn, H.: On a special class ofp-groups. Acta Math.100, 45–92 (1958).
Burnside, W.: Theory of Groups of Finite Order. Cambridge: University Press 1911.
Brauer, R.: Zur Darstellungstheorie der Gruppen endlichen Ordnung. Math. Z.63, 406–444 (1956).
—: Zur Darstellungstheorie der Gruppen endlichen Ordnung, II. Math. Z.72, 25–46 (1959).
—: Some applications of the theory of blocks of finite groups, I. J. Algebra1, 152–167 (1964).
—, andW. Fett: On the number of irreducible characters of finite groups in a given block. Proc. Natl. Acad. Sci.45, 361–365 (1959).
—, andC. Nesbitt: On the modular characters of groups. Ann. Math.42, 556–590 (1941).
Clifford, A.H.: Representations induced in an invariant subgroup. Ann. Math.38, 533–550 (1937).
Dickson, L.E.: Linear Groups with an Exposition of the Galois Field Theory. Leipzig: B. G. Teubner 1901.
Feit, W., andJ.G. Thompson: Solvability of groups of odd oder. Pac. J. Math.13, 771–1029 (1963).
Gorenstein, D., andJ.H. Walter: The characterization of finite groups with dihedral Sylow 2-subgroups, I. J. Algebra2, 85–162 (1965).
Huppert, B.: Gruppen mit modularen Sylow-Gruppe. Math. Z.75, 140–163 (1961).
Janko, Z.: A new finite simple group with abelian 2-Sylow groups and its characterization. J. Algebra3, 147–187 (1966).
—, andJ.G. Thompson: On a class of finite simple groups of Ree. J. Algebra4, 274–293 (1966).
Nagell, T.: Introduction to number theory. New York: John Wiley & Sons 1951.
Ree, R.: A family of simple groups associated with the Lie algebra of typeG 2. Am. J. Math.83, 432–462 (1961).
Schur, I.: Über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen. J. reine angew. Math.127, 20–50 (1904).
—: Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochen lineare Substitutionen. J. reine angew. Math.132, 85–137 (1907).
Suzuki, M.: Applications of group characters. Proc. Symp. Pure Math. Am. Math. Soc. 88–99 (1959).
—: Finite groups of even order in which Sylow 2-groups are independent. Ann. Math.80, 58–77 (1964).
Walter, J.H.: Character theory of finite groups with trivial intersection subsets. Nagoya Math. J.27, 515–525 (1966).
Walter, J.H.: The characterization of finite groups with abelian Sylow 2-subgroups (to appear).
Ward, H.N.: On Ree's series of simple groups. Trans. Am. Math. Soc.121, 62–89 (1966).
Wielandt, H.:p-Sylowgruppen undp-Faktogruppen. J. reine angew. Math.182, 180–193 (1940).
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ToJ. A. Dieudonn'e on the occasion of his sixtieth birthday
This research was undertaken while the author was supported by the National Science Foundation.
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Walter, J.H. Finite groups with abelian sylow 2-subgroups of order 8. Invent Math 2, 332–376 (1967). https://doi.org/10.1007/BF01428899
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DOI: https://doi.org/10.1007/BF01428899