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- W4211102616 abstract "Abstract Classical results from the theory of finite soluble groups state that Carter subgroups, i.e. self-normalizing nilpotent subgroups, coincide with nilpotent projectors and with nilpotent covering subgroups, and they form a non-empty conjugacy class of subgroups, in soluble groups. This paper presents an extension of these facts to $$pi $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>π</mml:mi> </mml:math> -separable groups, for sets of primes $$pi $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>π</mml:mi> </mml:math> , by proving the existence of a conjugacy class of subgroups in $$pi $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>π</mml:mi> </mml:math> -separable groups, which specialize to Carter subgroups within the universe of soluble groups. The approach runs parallel to the extension of Hall theory from soluble to $$pi $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>π</mml:mi> </mml:math> -separable groups by Čunihin, regarding existence and properties of Hall subgroups." @default.
- W4211102616 created "2022-02-13" @default.
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- W4211102616 date "2022-02-11" @default.
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- W4211102616 title "Carter and Gaschütz theories beyond soluble groups" @default.
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- W4211102616 doi "https://doi.org/10.1007/s13398-022-01215-7" @default.
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