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- W1969192103 abstract "(1) LO(G) Q G, (2) MPYW = Uz*), (3) MMW -N U,(q) x U,(q). After the fundamental work of Aschbacher [2] it becomes important to calssify groups with a standard subgroup L of known type, The aim of this paper is to classify the groups with a standard subgroup L of type U,(q), q = 2n > 2, whose centralizer has a cyclic Sylow 2-subgroup. As for U,(2), the readers are referred to Yamada [15]. The argument used for the proof of the theorem is similar to that of Gomi [9]. First we assume that O(G) = 1. In Section 3 arguing on the parabolic subgroups of L, we construct the corresponding parabolic subgroups of L,(q2) or U,(q) x Wd. For M?) we use a result of Timmesfeld [14] to obtain the conclusion in Section 4. For U,(q) x U,(q) in Section 5, after some transfer arguments, we apply a result of Goldschmidt [8] to prove the normality of the direct product. In the final section we give a short argument to remove the assumption that O(G) = 1. Our notation is standard and referred to in [lo] except possibly the following. If X is a 2-group," @default.
- W1969192103 created "2016-06-24" @default.
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- W1969192103 date "1980-06-01" @default.
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- W1969192103 title "Finite groups with a standard subgroup of type U5(2n), n > 1" @default.
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- W1969192103 doi "https://doi.org/10.1016/0021-8693(80)90155-6" @default.
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