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Conditions for Sylow 2-subgroups of the Fixed Point Subgroup Implying Solubility

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Abstract Let A and G be finite groups and suppose that A acts via automorphisms on G with $(|A|, |G|)=1$. We study how certain conditions on the Sylow 2-subgroups of… Click to show full abstract

Abstract Let A and G be finite groups and suppose that A acts via automorphisms on G with $(|A|, |G|)=1$. We study how certain conditions on the Sylow 2-subgroups of the fixed point subgroup of the action $C_G(A)$ may imply the non-simplicity or solubility of G.

Keywords: sylow subgroups; conditions sylow; subgroups fixed; point subgroup; fixed point

Journal Title: Proceedings of the Edinburgh Mathematical Society
Year Published: 2018

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