Groups with central -Sylow intersections of rank at most one

Authors:
Marcel Herzog and Ernest Shult

Journal:
Proc. Amer. Math. Soc. **38** (1973), 465-470

MSC:
Primary 20D05; Secondary 20D20

MathSciNet review:
0430055

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Abstract: An involution in a finite group is called central if it lies in the center of a -Sylow subgroup of . A -Sylow intersection is called central if it is either trivial or contains a central involution. Suppose is a finite simple group all of whose central -Sylow intersections are trivial or rank one -groups. It is proved that is a known simple group.

**1.**Michael Aschbacher,*A class of generalized 𝑇𝐼-groups*, Illinois J. Math.**16**(1972), 529–532. MR**0297864****[1]**George Glauberman,*Central elements in core-free groups*, J. Algebra**4**(1966), 403–420. MR**0202822****[2]**G. Glauberman,*Global and local properties of finite groups*, Finite simple groups (Proc. Instructional Conf., Oxford, 1969) Academic Press, London, 1971, pp. 1–64. MR**0352241****[3]**Marcel Herzog,*On 2-Sylow intersections*, Israel J. Math.**11**(1972), 326–327. MR**0301093****[4]**-,*Central -Sylow intersections*(to appear).**[5]**-,*Simple groups with cyclic central -Sylow intersections*(to appear).**[6]**V. D. Mazurov,*Finite simple groups with cyclic intersections of Sylow 2-subgroups*, Algebra i Logika**10**(1971), 188–198 (Russian). MR**0296157****[7]**P. Landrock,*Finite groups with Sylow -intersections of rank*, Aarhus University Preprint Series, no. 23 (to appear).**[8]**E. Shult,*On the fusion of an involution in its centralizer*(to appear).**[9]**E. Shult,*A note on Janko’s simple group of order 175,560*, Proc. Amer. Math. Soc.**35**(1972), 342–348. MR**0306303**, 10.1090/S0002-9939-1972-0306303-6

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0430055-3

Keywords:
Finite simple group,
-Sylow intersection

Article copyright:
© Copyright 1973
American Mathematical Society