On simple groups which are homomorphic images of multiplicative subgroups of simple algebras of degree 2

Michitaka HIKARI

doi:10.2969/jmsj/03530563

Michitaka HIKARI

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JOURNAL FREE ACCESS

1983 Volume 35 Issue 3 Pages 563-569

DOI https://doi.org/10.2969/jmsj/03530563

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Published: 1983 Received: July 12, 1982 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 simple groups of 2-rank two, Scripta Math., 29 (1973), 191-214.
2) S. Amitsur, Finite subgroups of division rings, Trans. Amer. Math. Soc., 80 (1955), 361-386.
3) C. Cato, The orders of the known simple groups as far as one trillion, Math. Comp., 31 (1977), 574-577.
4) L. Dornhoff, Group representation theory, Part A, Marcel Dekker, New York, 1971.
5) W. Feit, Characters of finite groups, Benjamin, New York, 1967.
6) D. Garbe and J.L. Mennicke, Some remarks on the Mathieu groups, Canad. Math. Bull., 7 (1964), 201-212.
7) D. Gorenstein and K. Harada, Finite groups whose 2-subgroups are generated by at most 4 elements, Mem. Amer. Math. Soc., 147, 1974.
8) R. Gow, Schur indices of some groups of Lie type, J. Algebra, 42 (1976), 102-120.
9) R. Griess, Schur multipliers of finite simple groups of Lie type, Trans. Amer. Math. Soc., 183 (1973), 355-421.
10) M. Hikari, Multiplicative p-subgroups of simple algebras, Osaka J. Math., 10 (1973), 369-374.
11) M. Hikari, On finite multiplicative subgroups of simple algebras of degree 2, J. Math. Soc. Japan, 28 (1976), 737-748.
12) B. Huppert, Endliche Gruppen I, Springer, Berlin, 1976.
13) G.J. Janusz, Simple components of QSL (2, q)), Comm. Algebra, 1 (1974), 1-22.
14) A.R. MacWilliams, On 2-groups with no normal abelian subgroups of rank 3, and their occurrence as Sylow 2-subgroups of finite simple groups, Trans. Amer. Math. Soc., 150 (1970), 345-408.
15) R. Steinberg, Lectures on Chevalley groups, Yale University Notes, New Haven, Conn., 1967.

Right : [1] J. L. Alperin, R. Brauer and D. Gorenstein, Finite simple groups of 2-rank two, Scripta Math., 29 (1973), 191-214.
[2] S. Amitsur, Finite subgroups of division rings, Trans. Amer. Math. Soc., 80 (1955), 361-386.
[3] C. Cato, The orders of the known simple groups as far as one trillion, Math. Comp., 31 (1977), 574-577.
[4] L. Dornhoff, Group representation theory, Part A, Marcel Dekker, New York, 1971.
[5] W. Feit, Characters of finite groups, Benjamin, New York, 1967.
[6] D. Garbe and J. L. Mennicke, Some remarks on the Mathieu groups, Canad. Math. Bull., 7 (1964), 201-212.
[7] D. Gorenstein and K. Harada, Finite groups whose 2-subgroups are generated by at most 4 elements, Mem. Amer. Math. Soc., 147, 1974.
[8] R. Gow, Schur indices of some groups of Lie type, J. Algebra, 42 (1976), 102-120.
[9] R. Griess, Schur multipliers of finite simple groups of Lie type, Trans. Amer. Math. Soc., 183 (1973), 355-421.
[10] M. Hikari, Multiplicative p-subgroups of simple algebras, Osaka J. Math., 10 (1973), 369-374.
[11] M. Hikari, On finite multiplicative subgroups of simple algebras of degree 2, J. Math. Soc. Japan, 28 (1976), 737-748.
[12] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1976.
[13] G. J. Janusz, Simple components of Q[SL (2, q)], Comm. Algebra, 1 (1974), 1-22.
[14] A. R. MacWilliams, On 2-groups with no normal abelian subgroups of rank 3, and their occurrence as Sylow 2-subgroups of finite simple groups, Trans. Amer. Math. Soc., 150 (1970), 345-408.
[15] R. Steinberg, Lectures on Chevalley groups, Yale University Notes, New Haven, Conn., 1967.

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