An elementary and unified approach to the Mathieu-Witt systems

Shiro IWASAKI

doi:10.2969/jmsj/04030393

Shiro IWASAKI

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JOURNAL FREE ACCESS

1988 Volume 40 Issue 3 Pages 393-414

DOI https://doi.org/10.2969/jmsj/04030393

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Published: 1988 Received: December 17, 1986 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: SUBTITLE Details: Wrong : Dedicated to Professor Nagayoshi Iwahori on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) T. Beth, Some remarks on D. R. Hughes' construction of M₁₂ and its associated designs, in “Finite geometries and designs”. London Math. Soc., Lecture Note, 49, Cambridge Univ. Press, London, 1981, pp. 22-30.
2) P. J. Cameron, Parallelisms of complete designs, London Math. Soc., Lecture Note, 23, Cambridge Univ. Press, London, 1976.
3) R. D. Carmichael, Introduction to the theory of groups of finite order, Ginn, Boston, 1937. (Reprint, Dover, New York, 1956.)
4) J. H. Conway, Three lectures on exceptional groups, in “Finite simple groups” (G. Higman and M. B. Powell, eds.), Academic Press, London-New York, 1971, pp. 215-247.
5) R. T. Curtis, A new combinatorial approach to M₂₄, Math. Proc. Cambridge Philos. Soc., 79(1976), 25-42.
6) R. T. Curtis, The Steiner system S(5, 6,12), the Mathieu group M₁₂ and the “Kitten”. in “Computational group theory” (M. D. Atkinson ed.), Academic Press, London-New York, 1984, pp. 353-358.
7) D. R. Hughes and F. C. Piper, Design theory, Cambridge Univ. Press, London, 1985.
8) B. Huppert, Endliche Gruppen I, Springer, 1967.
9) R. N. Lane, t-designs and t-ply homogeneous groups, J. Combin. Theory, 10 (1971), 106-118.
10) J. A. Todd, A representation of the Mathieu group M₂₄ as a collineation group, Ann. Mat. Pura. Appl., 71 (1966), 199-238.
11) T. Tsuzuku, Finite groups and finite geometries, Cambridge Univ. Press, London, 1982.
12) E. Witt, Die 5-fach transitiven Gruppen von Mathieu, Abh. Math. Sem. Univ. Hamburg, 12 (1938), 256-264.
13) E. Witt, Über Steinersche Systeme, Abh. Math. Sem. Univ. Hamburg, 265-275.

Right : [1] T. Beth, Some remarks on D. R. Hughes' construction of M₁₂ and its associated designs, in “Finite geometries and designs”. London Math. Soc., Lecture Note, 49, Cambridge Univ. Press, London, 1981, pp. 22-30.
[2] P. J. Cameron, Parallelisms of complete designs, London Math. Soc., Lecture Note, 23, Cambridge Univ. Press, London, 1976.
[3] R. D. Carmichael, Introduction to the theory of groups of finite order, Ginn, Boston, 1937. (Reprint, Dover, New York, 1956.)
[4] J. H. Conway, Three lectures on exceptional groups, in “Finite simple groups” (G. Higman and M. B. Powell, eds.), Academic Press, London-New York, 1971, pp. 215-247.
[5] R. T. Curtis, A new combinatorial approach to M₂₄, Math. Proc. Cambridge Philos. Soc., 79(1976), 25-42.
[6] R. T. Curtis, The Steiner system S (5, 6,12), the Mathieu group M₁₂ and the “Kitten”. in “Computational group theory” (M. D. Atkinson ed.), Academic Press, London-New York, 1984, pp. 353-358.
[7] D. R. Hughes and F. C. Piper, Design theory, Cambridge Univ. Press, London, 1985.
[8] B. Huppert, Endliche Gruppen I, Springer, 1967.
[9] R. N. Lane, t-designs and t-ply homogeneous groups, J. Combin. Theory, 10 (1971), 106-118.
[10] J. A. Todd, A representation of the Mathieu group M₂₄ as a collineation group, Ann. Mat. Pura. Appl., 71 (1966), 199-238.
[11] T. Tsuzuku, Finite groups and finite geometries, Cambridge Univ. Press, London, 1982.
[12] E. Witt, Die 5-fach transitiven Gruppen von Mathieu, Abh. Math. Sem. Univ. Hamburg, 12 (1938), 256-264.
[13] E. Witt, Über Steinersche Systeme, Abh. Math. Sem. Univ. Hamburg, 265-275.

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