On transitive groups in which the maximal number of fixed points of involutions is five

Yutaka HIRAMINE

doi:10.2969/jmsj/03020215

Yutaka HIRAMINE

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JOURNAL FREE ACCESS

1978 Volume 30 Issue 2 Pages 215-235

DOI https://doi.org/10.2969/jmsj/03020215

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Published: 1978 Received: July 07, 1975 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 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, Endliche zweifach transitive Permutationsgruppen, deren Involutionen keine Fixpunkte haben, Math. Z., 104 (1968), 175-204.
3) H. Bender, Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festläst, J. Algebra, 17 (1971), 527-554.
4) F. Buekenhout, Doubly transitive groups in which the maximum number of fixed points of involutions is four, to appear.
5) F. Buekenhout, Transitive groups in which involutions fix one or three points, J. Algebra, 23 (1972), 438-451.
6) F. Buekenhout and P. Rowlinson, On (1, 4)-groups II, to appear.
7) P. Fong, Sylow 2-subgroups of small order, to appear.
8) P. Fong and W. J. Wong, A characterization of the finite simple groups PS_p(4, q), G₂ (q), D₄²(q) I, Nagoya Math. J., 36 (1969), 143-184.
9) D. Gorenstein, Finite Groups, Harper and Row, New York, 1968.
10) D. Gorenstein and K. Harada, Finite groups whose 2-subgroup are generated by at most 4 elements, to appear.
11) K. Harada, On finite groups having self-centralizing 2-subgroups of small order, J. Algebra, 33 (1975), 144-160.
12) C. Hering, Zweifach transitive Permutationsgruppen, in denen 2 die maximal Anzahl von Fixpunkten von Involutionen ist, Math. Z., 104 (1968), 150-174.
13) B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin, 1968.
14) J. D. King, Doubly transitive groups in which involutions fix one or three points, Math. Z., 111 (1969), 311-321.
15) R. Noda, Doubly transitive groups in which the maximal number of fixed points of involutions is four, Osaka J. Math., 8 (1971), 77-90.
16) K. W. Phan, A characterization of four-dimensional unimodular groups, J. Algebra, 15 (1970), 252-279.
17) K.W. Phan, A characterization of the unitary groups PSU(4, q²), q odd, J. Algebra, 17 (1971), 132-148.
18) P. Rowlinson, Simple permutation groups in which an involution fixes a small number of points, J. London Math. Soc., (2) 4 (1972), 655-661.
19) P. Rowlinson, Simple permutation groups in which an involution fixes a small number of points II, to appear.
20) P. Rowlinson, On (1, 4) -groups I, to appear.
21) R. Steinburg, Automorphisms of finite linear groups, Canadian J. of Math., 12 (1960), 606-615.
22) W. J. Wong, A characterization of the finite projective symplectic groups PS_p4 (q), J. Algebra, 14 (1970), 1-35.

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, Endliche zweifach transitive Permutationsgruppen, deren Involutionen keine Fixpunkte haben, Math. Z., 104 (1968), 175-204.
[3] H. Bender, Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festläst, J. Algebra, 17 (1971), 527-554.
[4] F. Buekenhout, Doubly transitive groups in which the maximum number of fixed points of involutions is four, to appear.
[5] F. Buekenhout, Transitive groups in which involutions fix one or three points, J. Algebra, 23 (1972), 438-451.
[6] F. Buekenhout and P. Rowlinson, On (1, 4)-groups II, to appear.
[7] P. Fong, Sylow 2-subgroups of small order, to appear.
[8] P. Fong and W. J. Wong, A characterization of the finite simple groups PS_p(4, q), G₂ (q), D₄²(q) I, Nagoya Math. J., 36 (1969), 143-184.
[9] D. Gorenstein, Finite Groups, Harper and Row, New York, 1968.
[10] D. Gorenstein and K. Harada, Finite groups whose 2-subgroup are generated by at most 4 elements, to appear.
[11] K. Harada, On finite groups having self-centralizing 2-subgroups of small order, J. Algebra, 33 (1975), 144-160.
[12] C. Hering, Zweifach transitive Permutationsgruppen, in denen 2 die maximal Anzahl von Fixpunkten von Involutionen ist, Math. Z., 104 (1968), 150-174.
[13] B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin, 1968.
[14] J. D. King, Doubly transitive groups in which involutions fix one or three points, Math. Z., 111 (1969), 311-321.
[15] R. Noda, Doubly transitive groups in which the maximal number of fixed points of involutions is four, Osaka J. Math., 8 (1971), 77-90.
[16] K. W. Phan, A characterization of four-dimensional unimodular groups, J. Algebra, 15 (1970), 252-279.
[17] K. W. Phan, A characterization of the unitary groups PSU(4, q²), q odd, J. Algebra, 17 (1971), 132-148.
[18] P. Rowlinson, Simple permutation groups in which an involution fixes a small number of points, J. London Math. Soc., (2) 4 (1972), 655-661.
[19] P. Rowlinson, Simple permutation groups in which an involution fixes a small number of points II, to appear.
[20] P. Rowlinson, On (1, 4) -groups I, to appear.
[21] R. Steinburg, Automorphisms of finite linear groups, Canadian J. of Math., 12 (1960), 606-615.
[22] W. J. Wong, A characterization of the finite projective symplectic groups PS_p₄ (q), J. Algebra, 14 (1970), 1-35.

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