A characterization of the groups PSL(3, 2n) and PSp(4, 2n)

Kensaku GOMI

doi:10.2969/jmsj/02630549

A characterization of the groups PSL(3, 2ⁿ) and PSp(4, 2ⁿ)

Kensaku GOMI

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1974 Volume 26 Issue 3 Pages 549-574

DOI https://doi.org/10.2969/jmsj/02630549

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Published: 1974 Received: October 05, 1973 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. L. Alperin, R. Brauer and D. Gorenstein, Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups, Trans. Amer. Math. Soc., 151 (1970), 1-261.
2) H. Bender, Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festläßt, J. Algebra, 17 (1971), 525-554.
3) R. Brauer and M. Suzuki, On finite groups of even order whose 2-Sylow group is a generalized quaternion group, Proc. Nat. Acad. Sci., 45 (1959), 1757-1759.
4) W. Feit and J. G. Thompson, Solvability of groups of odd order, Pacific J. Math., 13 (1963), 755-1029.
5) D. M. Goldschmidt, 2-Fusion in finite groups, to appear.
6) D. Gorenstein, Finite groups, Harper and Row, New York, 1968.
7) D. Gorenstein, On finite simple groups of characteristic 2 type, Inst. Hautes Études Sci. Publ. Math., 36 (1969), 5-13.
8) D. Gorenstein and J. Walter, The characterization of finite groups with dihedral Sylow 2-subgroups, J. Algebra, 2 (1965), 85-151, 218-270, 354-393.
9) K. Harada, Groups with a certain type of Sylow 2-subgroups, J. Math. Soc. Japan, 19 (1967), 303-307.
10) D. G. Higman, Finite permutation groups of rank 3, Math. Z., 86 (1964), 145-156.
11) M. Suzuki, A characterization of the simple groups LF(2, p), J. Fac. Sci. Univ. Tokyo, 6 (1951), 259-293.
12) M. Suzuki, Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc., 99 (1961), 425-470.
13) M. Suzuki, Finite groups of even order in which Sylow 2-subgroups are independent, Ann, of Math., 80 (1964), 58-77.
14) M. Suzuki, Finite groups in which the centralizer of any element of order 2 is 2-closed, Ann. of Math., 82 (1965), 191-212.
15) J. G. Thompson, Non-solvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc., 74 (1968), 383-437.

Right : [1] J. L. Alperin, R. Brauer and D. Gorenstein, Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups, Trans. Amer. Math. Soc., 151 (1970), 1-261.
[2] H. Bender, Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festläßt, J. Algebra, 17 (1971), 525-554.
[3] R. Brauer and M. Suzuki, On finite groups of even order whose 2-Sylow group is a generalized quaternion group, Proc. Nat. Acad. Sci., 45 (1959), 1757-1759.
[4] W. Feit and J. G. Thompson, Solvability of groups of odd order, Pacific J. Math., 13 (1963), 755-1029.
[5] D. M. Goldschmidt, 2-Fusion in finite groups, to appear.
[6] D. Gorenstein, Finite groups, Harper and Row, New York, 1968.
[7] D. Gorenstein, On finite simple groups of characteristic 2 type, Inst. Hautes Études Sci. Publ. Math., 36 (1969), 5-13.
[8] D. Gorenstein and J. Walter, The characterization of finite groups with dihedral Sylow 2-subgroups, J. Algebra, 2 (1965), 85-151, 218-270, 354-393.
[9] K. Harada, Groups with a certain type of Sylow 2-subgroups, J. Math. Soc. Japan, 19 (1967), 303-307.
[10] D. G. Higman, Finite permutation groups of rank 3, Math. Z., 86 (1964), 145-156.
[11] M. Suzuki, A characterization of the simple groups LF(2, p), J. Fac. Sci. Univ. Tokyo, 6 (1951), 259-293.
[12] M. Suzuki, Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc., 99 (1961), 425-470.
[13] M. Suzuki, Finite groups of even order in which Sylow 2-subgroups are independent, Ann. of Math., 80 (1964), 58-77.
[14] M. Suzuki, Finite groups in which the centralizer of any element of order 2 is 2-closed, Ann. of Math., 82 (1965), 191-212.
[15] J. G. Thompson, Non-solvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc., 74 (1968), 383-437.

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