Coprime automorphisms of finite groups
نویسندگان
چکیده
Let G G be a finite group admitting coprime automorphism alttext="alpha"> α encoding="application/x-tex">\alpha of order alttext="e"> e encoding="application/x-tex">e . Denote by I Subscript upper G Baseline left-parenthesis alpha right-parenthesis"> I ( stretchy="false">) encoding="application/x-tex">I_G(\alpha ) the set commutators alttext="g Superscript negative 1 g alpha"> g − 1 encoding="application/x-tex">g^{-1}g^\alpha , where element-of ∈<!-- ∈ encoding="application/x-tex">g\in G and alttext="left-bracket comma right-bracket"> stretchy="false">[ , stretchy="false">] encoding="application/x-tex">[G,\alpha ] subgroup generated We study impact on structure Suppose that each subset can at most alttext="r"> r encoding="application/x-tex">r elements. show rank is alttext="left-parenthesis e r encoding="application/x-tex">(e,r) -bounded. Along way, we establish several results independent interest. In particular, prove if every element has odd order, then too. Further, pair elements from generates soluble, or nilpotent, subgroup, respectively nilpotent.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2022
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/tran/8553