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- W2019802807 abstract "In Part I of this paper (Hering, Kantor, and Seitz [SO]), 2-transitive groups of even degree were classified when the stabilizer of a point has a normal subgroup regular on the remaining points. The identification with groups of known type was made by finding a 2-Sylow subgroup and then applying the deep classification theorems of Alperin, Brauer and Gorenstein [l, 21 and Walter [39]. The purpose of the present continuation of [50] is to point out that the proof of the main result of [50] can be completed without using [I] and [2]. 1Ioreover, Walter’s classification theorem [39] and the Gorenstein-Walter Theorem [49] are not required in [50], although the end of Walter [53] seems to be needed. Our arguments are natural continuations of those of [50, Sections 4, 8, and 91. Much use is also made of character-theoretic information contained in Brauer [46] and [47]. Our goal is to show that a minimal counteresamplc has a cyclic two points stabilizer G,,, and then apply a result of Kantor, O’Nan and Seitz [22, Theorem 1.1 or Section 5, Case D]. Re first show that G,, is metacyclic, and then “transfer out field automorphisms” in order to prove that G,, is cyclic. This transfer argument yielded an unexpected dividend: in the course of examining a similar argument in Suzuki [34, Section 211, an error was found. This has been corrected, and, in fact, the entire transfer argument is stated for odd and even degree groups simultaneously. ‘Phc numbering of both the sections and the references will be continued from [50]." @default.
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- W2019802807 title "Finite groups with a split BN-pair of rank 1. I" @default.
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- W2019802807 doi "https://doi.org/10.1016/0021-8693(72)90068-3" @default.
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