A sufficient condition for fixed points of a coprime action to have a normal complement
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Let A be a finite group acting on a finite group G via automorphisms. Assume that \((|A|,|G|)=1\). We prove that if \(C_G(A)\) is a Hall \(\pi \)-subgroup of G, then G has a normal \(\pi \)-complement.
KeywordsCoprime action Normal complement
Mathematics Subject Classification20D10 20D20
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The author would like to thank an anonymous referee for many invaluable suggestions on the original manuscript.
- 3.Isaacs, I.M.: Finite Group Theory. Graduate Studies in Mathematics, vol. 92. American Mathematical Society, Providence (2008)Google Scholar