A note on Sylow intersections
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- by Ariel Ish-Shalom PDF
- Proc. Amer. Math. Soc. 66 (1977), 227-230 Request permission
Abstract:
Let p be a prime number, G a finite group whose order is divisible by p, and S a Sylow p-subgroup of G. We say that G satisfies $( \ast )$ if there exists $g \in G$ such that $S \cap {S^g} = {O_p}(G)$. There are examples of primes p and finite groups G that do not satisfy $( \ast )$. In this note we discuss several related properties satisfied in general, as well as giving sufficient conditions for G to satisfy $( \ast )$.References
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- Marcel Herzog, Intersections of nilpotent Hall subgroups, Pacific J. Math. 36 (1971), 331–333. MR 280595
- Marcel Herzog, On Sylow intersections, Proc. Amer. Math. Soc. 37 (1973), 352–354. MR 310055, DOI 10.1090/S0002-9939-1973-0310055-4
- Noboru Itô, Über den kleinsten $p$-Durchschnitt auflösbarer Gruppen, Arch. Math. (Basel) 9 (1958), 27–32 (German). MR 131455, DOI 10.1007/BF02287057
- Thomas J. Laffey, A remark on minimal Sylow intersections, Bull. London Math. Soc. 4 (1972), 377. MR 318306, DOI 10.1112/blms/4.3.377
- Thomas J. Laffey, On minimal Sylow intersections, J. London Math. Soc. (2) 12 (1975/76), no. 3, 383–384. MR 393226, DOI 10.1112/jlms/s2-12.3.383
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 227-230
- MSC: Primary 20D20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0460460-4
- MathSciNet review: 0460460