On some doubly transitive permutation groups of degree n and order 2l(n-1)n

Hiroshi KIMURA

doi:10.2969/jmsj/02230263

On some doubly transitive permutation groups of degree n and order 2^l(n-1)n

Hiroshi KIMURA

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JOURNAL FREE ACCESS

1970 Volume 22 Issue 3 Pages 263-277

DOI https://doi.org/10.2969/jmsj/02230263

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Published: 1970 Received: January 27, 1969 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) W. Feit, On class of doubly transitive permutation groups, Illinois J. Math., 4 (1960), 170-186.
2) W. Feit and J. G. Thompson, Solvability of groups of odd order, Pacific J. Math., 13 (1963), 775-1029.
3) P. Fong, Some Sylow subgroups of order 32 and a characterization of U(3, 3), J. Algebra, 6 (1967), 65-76.
4) D. Gorenstein, Finite groups, Harper and Row, New York, 1968.
5) D. Gorenstein and J. H. Walter, The characterization of finite groups with dihedral Sylow 2-subgroups, I, II, III, J. Algebra, 2 (1965), 85-151, 218-270, 334-393.
6) K. Harada, A characterization of the simple group U₃(5), Nagoya Math. J. (to appear).
7) B. Huppert, Endliche Gruppen I, Springer, Berlin, 1968.
8) N. Ito, On a class of doubly transitive permutation groups, Illinois J. Math., 6 (1962), 341-352.
9) N. Ito, On doubly transitive groups of degree n and order 2(n-1)n, Nagoya Math. J., 27 (1966), 409-417.
10) H. Kimura, On doubly transitive permutation groups of degree n and order 4(n-1)n, J. Math. Soc. Japan, 21 (1969), 234-243.
11) H. Lüneburg, Charakterisierungen der endlichen desarguesschen projektiven Ebenen, Math. Z., 85 (1964), 419-450.
12) R. Ree, Sur une famille de groupes de permutations doublement transitifs, Canad. J. Math., 16 (1964), 797-819.
13) W. R. Scott, Group theory, Prentice-Hall, Englewood Cliffs, N. J., 1964.
14) M. Suzuki, On a class of doubly transitive groups, Ann. of Math., 75 (1962), 105-145.
15) M. Suzuki, A characterization of the 3-dimensional projective unitary group over a finite field of odd characteristic, J. Algebra, 2 (1965), 1-14.
16) H. N. Ward, On Ree's series of simple groups, Trans. Amer. Math. Soc., 121 (1966), 62-89.
17) H. Wielandt, Finite permutation groups, Academic Press, New York, 1964.
18) H. Zassenhaus, Kennzeichung endlicher linearer Gruppen als Permutations-gruppen, Abh. Math. Sem. Univ. Hamburg, 11 (1936), 17-40.

Right : [1] W. Feit, On class of doubly transitive permutation groups, Illinois J. Math., 4 (1960), 170-186.
[2] W. Feit and J. G. Thompson, Solvability of groups of odd order, Pacific J. Math., 13 (1963), 775-1029.
[3] P. Fong, Some Sylow subgroups of order 32 and a characterization of U(3, 3), J. Algebra, 6 (1967), 65-76.
[4] D. Gorenstein, Finite groups, Harper and Row, New York, 1968.
[5] D. Gorenstein and J. H. Walter, The characterization of finite groups with dihedral Sylow 2-subgroups, I, II, III, J. Algebra, 2 (1965), 85-151, 218-270, 334-393.
[6] K. Harada, A characterization of the simple group U₃(5), Nagoya Math. J. (to appear).
[7] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1968.
[8] N. Ito, On a class of doubly transitive permutation groups, Illinois J. Math., 6 (1962), 341-352.
[9] N. Ito, On doubly transitive groups of degree n and order 2(n-1)n, Nagoya Math. J., 27 (1966), 409-417.
[10] H. Kimura, On doubly transitive permutation groups of degree n and order 4(n-1)n, J. Math. Soc. Japan, 21 (1969), 234-243.
[11] H. Lüneburg, Charakterisierungen der endlichen desarguesschen projektiven Ebenen, Math. Z., 85 (1964), 419-450.
[12] R. Ree, Sur une famille de groupes de permutations doublement transitifs, Canad. J. Math., 16 (1964), 797-819.
[13] W. R. Scott, Group theory, Prentice-Hall, Englewood Cliffs, N. J., 1964.
[14] M. Suzuki, On a class of doubly transitive groups, Ann. of Math., 75 (1962), 105-145.
[15] M. Suzuki, A characterization of the 3-dimensional projective unitary group over a finite field of odd characteristic, J. Algebra, 2 (1965), 1-14.
[16] H. N. Ward, On Ree's series of simple groups, Trans. Amer. Math. Soc., 121 (1966), 62-89.
[17] H. Wielandt, Finite permutation groups, Academic Press, New York, 1964.
[18] H. Zassenhaus, Kennzeichung endlicher linearer Gruppen als Permutations-gruppen, Abh. Math. Sem. Univ. Hamburg, 11 (1936), 17-40.

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