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- W2022879947 abstract "It is shown that in certain classes of finite groups, inner automorphisms are characterized by an extension property and also by a dual lifting property. This is a consequence of the fact that for any finite group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and any prime <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, there is a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding=application/x-tex>P</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and a semidirect product <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H equals upper G upper P> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>=</mml:mo> <mml:mi>G</mml:mi> <mml:mi>P</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>H = GP</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding=application/x-tex>P</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is characteristic in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding=application/x-tex>H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and every automorphism of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding=application/x-tex>H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> induces an inner automorphism on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H slash upper P> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>H/P</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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- W2022879947 date "1989-01-01" @default.
- W2022879947 modified "2023-09-25" @default.
- W2022879947 title "On inner automorphisms of finite groups" @default.
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