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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
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$.

References [Enhancements On Off] (What's this?)

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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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