Sylow 2-intersections, 2-fusion, and 2-factorizations in finite groups of characteristic 2 type

Kensaku GOMI

doi:10.2969/jmsj/03540571

Kensaku GOMI

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JOURNAL FREE ACCESS

1983 Volume 35 Issue 4 Pages 571-588

DOI https://doi.org/10.2969/jmsj/03540571

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Published: 1983 Received: February 19, 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, Sylow intersections and fusion, J. Algebra, 6(1967), 222-241.
2) M. Aschbacher, On the failure of the Thompson factorization in 2-constrained groups, Proc. London Math. Soc., 43 (1981), 425-449.
3) M. Aschbacher, A factorization theorem for 2-constrained groups, Proc. London Math. Soc., 43 (1981), 450-477.
4) M. Aschbacher, GF (2)-representations of finite groups, Amer. J. Math., 104 (1982), 683-771.
5) M. Aschbacher, D. Gorenstein and R. Lyons, The embedding of 2-locals in finite groups of characteristic 2-type, Ann. of Math., 114(1981), 335-456.
6) B. Baumann, Über endliche Gruppen mit einer zu L₂(2ⁿ) isomorphen Factorgruppe, Proc. Amer. Math. Soc., 74 (1979), 215-222.
7) N. R. Campbell, Pushing up in finite groups, Ph. D. Thesis, California Institute of Technology, 1979.
8) R. Foote, Component type theorems for finite groups in characteristic 2, Illinois J. Math., 26 (1982), 62-111.
9) G. Glauberman and R. Niles, A pair of characteristic subgroups for pushing-up in finite groups, Proc. London Math. Soc. (to appear).
10) D. M. Goldschmidt, A conjugation family for finite groups, J. Algebra, 16(1970), 138-142.
11) K. Gomi, A characterization of the groups PSL (3, 2ⁿ)) and PSp (4, 2ⁿ), J. Math. Soc. Japan, 26 (1974), 549-574.
12) K. Gomi, Sylow 2-intersections and split BN-pairs of rank two, J. Fac. Sci. Univ. Tokyo Sect. IA, 23 (1976), 1-22.
13) K. Gomi, Control of Sylow 2-intersections in groups of Chev (2) type and groups of alternating type, Sci. Papers College Gen. Ed. Univ. Tokyo, 32(1982), 15-31.
14) K. Gomi, On GF (2) -representations of finite groups, “Group Theory and Its Applications”. Reports on Researches Supported by Grant-in-Aid for Scientific Research No. 56460001 (ed. T. Kondo), College of General Education, Univ. Tokyo, 1983.
15) D. Gorenstein and J. H. Walter, Balance and generation in finite groups, J. Algebra, 33(1975), 224-287.
16) T. Kondo, On Alperin-Goldschmidt's fusion theorem, Sci. Papers College Gen. Ed. Univ. Tokyo, 28 (1978), 159-166.
17) R. Solomon, On certain 2-local blocks (to appear).
18) R. Solomon and S. K. Wong, On L₂ (2ⁿ) -blocks (to appear).

Right : [1] J. L. Alperin, Sylow intersections and fusion, J. Algebra, 6 (1967), 222-241.
[2] M. Aschbacher, On the failure of the Thompson factorization in 2-constrained groups, Proc. London Math. Soc., 43 (1981), 425-449.
[3] M. Aschbacher, A factorization theorem for 2-constrained groups, Proc. London Math. Soc., 43 (1981), 450-477.
[4] M. Aschbacher, GF (2)-representations of finite groups, Amer. J. Math., 104 (1982), 683-771.
[5] M. Aschbacher, D. Gorenstein and R. Lyons, The embedding of 2-locals in finite groups of characteristic 2-type, Ann. of Math., 114 (1981), 335-456.
[6] B. Baumann, Über endliche Gruppen mit einer zu L₂(2ⁿ) isomorphen Factorgruppe, Proc. Amer. Math. Soc., 74 (1979), 215-222.
[7] N. R. Campbell, Pushing up in finite groups, Ph. D. Thesis, California Institute of Technology, 1979.
[8] R. Foote, Component type theorems for finite groups in characteristic 2, Illinois J. Math., 26 (1982), 62-111.
[9] G. Glauberman and R. Niles, A pair of characteristic subgroups for pushing-up in finite groups, Proc. London Math. Soc. (to appear).
[10] D. M. Goldschmidt, A conjugation family for finite groups, J. Algebra, 16 (1970), 138-142.
[11] K. Gomi, A characterization of the groups PSL (3, 2ⁿ)) and PSp (4, 2ⁿ), J. Math. Soc. Japan, 26 (1974), 549-574.
[12] K. Gomi, Sylow 2-intersections and split BN-pairs of rank two, J. Fac. Sci. Univ. Tokyo Sect. IA, 23 (1976), 1-22.
[13] K. Gomi, Control of Sylow 2-intersections in groups of Chev (2) type and groups of alternating type, Sci. Papers College Gen. Ed. Univ. Tokyo, 32 (1982), 15-31.
[14] K. Gomi, On GF (2)-representations of finite groups, “Group Theory and Its Applications”. Reports on Researches Supported by Grant-in-Aid for Scientific Research No. 56460001 (ed. T. Kondo), College of General Education, Univ. Tokyo, 1983.
[15] D. Gorenstein and J. H. Walter, Balance and generation in finite groups, J. Algebra, 33 (1975), 224-287.
[16] T. Kondo, On Alperin-Goldschmidt's fusion theorem, Sci. Papers College Gen. Ed. Univ. Tokyo, 28 (1978), 159-166.
[17] R. Solomon, On certain 2-local blocks (to appear).
[18] R. Solomon and S. K. Wong, On L₂(2ⁿ)-blocks (to appear).

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