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An odd order remark - MaRDI portal

An odd order remark (Q912977)

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scientific article; zbMATH DE number 4146237
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English
An odd order remark
scientific article; zbMATH DE number 4146237

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    An odd order remark (English)
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    1990
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    The author gives a short proof that in a minimal counterexample to the odd order theorem of \textit{W. Feit} and \textit{J. Thompson} [Pac. J. Math. 13, 775-1029 (1963; Zbl 0124.26402)] there is a strongly p-embedded subgroup, where p is the smallest prime dividing the order. For a proof of the more sharper theorems in chapter IV of the odd order paper due to \textit{H. Bender} see [Ill. J. Math. 14, 376-384 (1970; Zbl 0218.20014)]. For the proof of his result the author just uses basic results in group theory like Alperin's Fusion Theorem and Glauberman's ZJ-Theorem and the solvable signalizer theorem.
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    uniqueness
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    simple groups
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    odd order theorem
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    p-embedded subgroup
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    Alperin's Fusion Theorem
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    Glauberman's ZJ-Theorem
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    solvable signalizer theorem
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