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Finite simple groups with short chains of subgroups
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1968 Volume 20 Issue 4 Pages 655-672
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- Published: 1968 Received: March 25, 1968 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. Brauer, On finite Desarguesian planes. II, Math. Zeit., 91 (1966), 124-151.
2) R. Brauer, Some applications of the theory of blocks of characters of finite groups. II, J. Algebra, 1 (1964), 307-334, III., J. Algebra, 3 (1966), 225-255.
3) R. Brauer and P. Fong, A characterization of the Mathieu group M12 of degree 12, Trans. Amer. Math. Soc., 122 (1966), 18-47.
4) R. Brauer and M. Suzuki, On finite groups of even order whose 2-Sylow group is a quaternion group, Proc. Nat. Acad. Sci. U.S.A., 45 (1959), 1757-1759.
5) W. Feit and J.G. Thompson, Solvability of groups of odd order, Pac. J. Math., 13 (1963), 775-1029.
6) P. Fong, Some Sylow subgroups of order 32 and a characterization of U(3, 3), J. Algebra, 6 (1967), 65-76.
7) P. Fong, Sylow 2-subgroups of small order I, II, (to appear).
8) W. Gaschütz, Zur Erweiterung theorie der endlichen Gruppen, J. reine angew. Math., 190 (1952), 93-107.
9) G. Glauberman, Central elements in core free groups, J. Algebra, 4 (1966), 403-420.
10) D. Gorenstein, Finite group in which Sylow 2-subgroups are abelian and centralizers of involutions are solvable, Canad. J. Math., 17 (1965), 860-906.
11) D. Gorenstein and J. Walter, The characterization of finite groups with dihedral Sylow 2-subgroups. I, II, III, J. Algebra, 2 (1965), 85-151, 218-270, 364-393.
12) J. A. Green, Blocks of modular representations of a finite group, Math. Zeit., 70 (1959), 430-445.
13) M. Hall, A search for simple groups of orders less than one million (to appear).
14) M. Hall and J. K. Senior, The groups of order 2n (n_??_6), Macmillan, New York, 1964.
15) K. Harada, A characterization of the simple group U3(5) (to appear).
16) Z. Janko, Finite groups with invariant fourth maximal subgroups, Math. Zeit., 82 (1963), 82-89.
17) Z. Janko, Finite simple groups with short chains of subgroups, Math. Zeit., 84 (1964), 428-437.
18) Z. Janko, A new finite simple group with abelian Sylow 2-subgroups and its characterization, J. Algebra, 3 (1966), 147-186.
19) Z. Janko and J.G. Thompson, On a class of finite simple groups on Ree, J. Algebra, 4 (1966), 274-292.
20) I. Schur, Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. reine angew. Math., 132 (1907), 85-137.
21) M. Suzuki, Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc., 69 (1961), 425-470.
22) M. Suzuki, A characterization of the 3-dimensional projective unitary group over a finite field of odd characteristic, J. Algebra, 2 (1965), 1-14.
23) J. G. Thompson, A special class of non-solvable groups, Math. Zeit., 72 (1960), 458-462.
24) H. Ward, On Ree's series of simple groups, Trans. Amer. Math. Soc., 121 (1966), 62-89.
25) J. Walter, Finite groups with abelian Sylow 2-subgroups of order 8, Invent. Math., 2 (1967), 332-376.
26) W. J. Wong, On finite groups whose 2-sylow subgroups have cyclic subgroups of index 2, J. Austral. Math. Soc., 4 (1964), 90-112.
Right : [1] R. Brauer, On finite Desarguesian planes. II, Math. Zeit., 91 (1966), 124-151.
[2] R. Brauer, Some applications of the theory of blocks of characters of finite groups. II, J. Algebra, 1 (1964), 307-334, III., J. Algebra, 3 (1966), 225-255.
[3] R. Brauer and P. Fong, A characterization of the Mathieu group M12 of degree 12, Trans. Amer. Math. Soc., 122 (1966), 18-47.
[4] R. Brauer and M. Suzuki, On finite groups of even order whose 2-Sylow group is a quaternion group, Proc. Nat. Acad. Sci. U. S. A., 45 (1959), 1757-1759.
[5] W. Feit and J. G. Thompson, Solvability of groups of odd order, Pac. J. Math., 13 (1963), 775-1029.
[6] P. Fong, Some Sylow subgroups of order 32 and a characterization of U(3, 3), J. Algebra, 6 (1967), 65-76.
[7] P. Fong, Sylow 2-subgroups of small order I, II, (to appear).
[8] W. Gaschütz, Zur Erweiterung theorie der endlichen Gruppen, J. reine angew. Math., 190 (1952), 93-107.
[9] G. Glauberman, Central elements in core free groups, J. Algebra, 4 (1966), 403-420.
[10] D. Gorenstein, Finite group in which Sylow 2-subgroups are abelian and centralizers of involutions are solvable, Canad. J. Math., 17 (1965), 860-906.
[11] D. Gorenstein and J. Walter, The characterization of finite groups with dihedral Sylow 2-subgroups. I, II, III, J. Algebra, 2 (1965), 85-151, 218-270, 364-393.
[12] J. A. Green, Blocks of modular representations of a finite group, Math. Zeit., 70 (1959), 430-445.
[13] M. Hall, A search for simple groups of orders less than one million (to appear).
[14] M. Hall and J. K. Senior, The groups of order 2n (n≤6), Macmillan, New York, 1964.
[15] K. Harada, A characterization of the simple group U3(5) (to appear).
[16] Z. Janko, Finite groups with invariant fourth maximal subgroups, Math. Zeit., 82 (1963), 82-89.
[17] Z. Janko, Finite simple groups with short chains of subgroups, Math. Zeit., 84 (1964), 428-437.
[18] Z. Janko, A new finite simple group with abelian Sylow 2-subgroups and its characterization, J. Algebra, 3 (1966), 147-186.
[19] Z. Janko and J. G. Thompson, On a class of finite simple groups on Ree, J. Algebra, 4 (1966), 274-292.
[20] I. Schur, Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. reine angew. Math., 132 (1907), 85-137.
[21] M. Suzuki, Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc., 69 (1961), 425-470.
[22] M. Suzuki, A characterization of the 3-dimensional projective unitary group over a finite field of odd characteristic, J. Algebra, 2 (1965), 1-14.
[23] J. G. Thompson, A special class of non-solvable groups, Math. Zeit., 72 (1960), 458-462.
[24] H. Ward, On Ree's series of simple groups, Trans. Amer. Math. Soc., 121 (1966), 62-89.
[25] J. Walter, Finite groups with abelian Sylow 2-subgroups of order 8, Invent. Math., 2 (1967), 332-376.
[26] W. J. Wong, On finite groups whose 2-sylow subgroups have cyclic subgroups of index 2, J. Austral. Math. Soc., 4 (1964), 90-112.
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