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A GENERALIZED FIXED-POINT-FREE ACTION
Date
2013-05-01
Author
Güloğlu, İsmail Şuayip
Ercan, Gülin
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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.
Subject Keywords
Solvable
,
Nilpotent height
,
Automorphism
,
Fixed point free action
URI
https://hdl.handle.net/11511/42052
Journal
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
DOI
https://doi.org/10.1142/s0219498812501721
Collections
Department of Mathematics, Article
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A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h is an element of H. Suppose that a finite group G admits a Frobenius-like group of auto-morphisms FH of coprime order with [F', H] = 1. In case where C-G( F) = 1 we prove that the groups G and C-G( H) have the same nilpotent length under certain additional assumptions.
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Ercan, Gülin; Ogut, Elif (2014-01-01)
We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C-CG(F) (h) = 1 for all nonidentity elements h is an element of H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.
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BibTeX
İ. Ş. Güloğlu and G. Ercan, “A GENERALIZED FIXED-POINT-FREE ACTION,”
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
, pp. 0–0, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42052.