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On Sylow intersections

Published online by Cambridge University Press:  17 April 2009

Ariel Ish-Shalom
Ariel Ish-Shalom
Affiliation:
Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel.
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Abstract

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Let G be a finite group, p a prime divisor of |G|, and T a p–subgroup of G. Define σ(T) to be the number of Sylow p–subgroups of G containing T. Call T a central p–Sylow intersection if for some Σ ⊆ Sylp (G), T = ∩(S | S є Σ), and if, in addition, T contains the center of a Sylow p–subgroup of G. This work is inspired and motivated by work of G. Stroth [J. Algebra 37 (1975), 111–120]. Generalizing an argument of his we describe finite groups in which every central p–Sylow intersection T with p–rank(T) > 2 satisfies σ(T) ≤ p.

Related methods yield the description of finite groups in which every central p–Sylow intersection T with p–rank(T) ≥ 2 satisfies σ(T) ≤ 2p.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 2 , April 1977 , pp. 237 - 246
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Alperin, J.L., “Sylow intersections and fusion”, J. Algebra 6 (1967), 222–214.CrossRefGoogle Scholar
[2]Alperin, J.L., “Up and down fusion”, J. Algebra 28 (1974), 206–209.CrossRefGoogle Scholar
[3]Alperin, J.L., Brauer, Richard, Gorenstein, Daniel, “Finite simple groups of 2-rank two”, Scripta Math. 29 (1973), 191–214.Google Scholar
[4]Goldschmidt, David M., “2-fusion in finite groups”, Ann. of Math. (2) 99 (1974), 70–117.CrossRefGoogle Scholar
[5]Gomi, Kensaku, “Finite groups with central Sylow 2-intersections”, J. Math. Soc. Japan 25 (1973), 342–355.Google Scholar
[6]Herzog, Marcel and Shult, Ernest, “Groups with central 2-Sylow intersections of rank at most one”, Proc. Amer. Math. Soc. 38 (1973), 465–470.CrossRefGoogle Scholar
[7]Huppert, B., Endliche Gruppen I (Die Grundlehren der mathematischen Wissenschaften, 134. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[8]Ish-Shalom, Ariel, “On 2-Sylow intersections”, Israel J. Math. 18 (1974), 235–242.CrossRefGoogle Scholar
[9]Ish-Shalom, Ariel, “On central 2-Sylow intersections”, submitted.Google Scholar
[10]Stroth, G., “Eine Kennzeichnung der 2I-Gruppen”, J. Algebra 37 (1975), 111–120.CrossRefGoogle Scholar
[11]Suzuki, Michio, “A characterization of simple groups LF(2, p)”, J. Fac. Sci. Univ. Tokyo Sect. I 6 (1951), 259–293.Google Scholar