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A generalized fixed point free automorphism of prime power order
Date
2012-06-01
Author
Ercan, Gülin
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Let G be a finite group and alpha be an automorphism of G of order p(n) for an odd prime p. Suppose that alpha acts fixed point freely on every alpha-invariant p'-section of G, and acts trivially or exceptionally on every elementary abelian alpha-invariant p-section of G. It is proved that G is a solvable p-nilpotent group of nilpotent length at most n + 1, and this bound is best possible.
Subject Keywords
Noncoprime automorphism
,
Nilpotent length
,
P-length
,
Exceptional action
URI
https://hdl.handle.net/11511/43870
Journal
International Journal of Algebra and Computation
DOI
https://doi.org/10.1142/s0218196712500294
Collections
Department of Mathematics, Article
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In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x epsilon C-G(A) of prime order or of order 4, every conjugate of x in G is also contained in C-G(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.
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G. Ercan, “A generalized fixed point free automorphism of prime power order,”
International Journal of Algebra and Computation
, pp. 0–0, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43870.