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Automorphism of a finite group scalar on the cosets of a subgroup


Author: Saïd Sidki
Journal: Proc. Amer. Math. Soc. 32 (1972), 399-402
MSC: Primary 20D45
DOI: https://doi.org/10.1090/S0002-9939-1972-0301096-0
MathSciNet review: 0301096
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Abstract: Let G be a finite group, $ \sigma $ an automorphism of G, M a $ \sigma $-invariant subgroup of G, and n a fixed integer. If $ \sigma (g) \in {g^n}M$ for all $ g \in G$ then there exists a $ \sigma $-invariant normal subgroup K of G, contained in M, with $ \sigma (g) \in {g^n}K$ for all $ g \in G$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0301096-0
Keywords: Scalar automorphism, fixed point free automorphism, Engel element, Baer's theorem, Odd Order paper, involution, simple group
Article copyright: © Copyright 1972 American Mathematical Society

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