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Finite groups having centralizer commutator product property
Date
2015-12-01
Author
Ercan, Gülin
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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Let a be an automorphism of a finite group G and assume that G = {[g, alpha] : g is an element of G} . C-G(alpha). We prove that the order of the subgroup [G, alpha] is bounded above by n(log2(n+1)) where n is the index of C-G(alpha) in G.
Subject Keywords
Automorphism
,
Commutator
,
Fixed point subgroup
,
Centralizer
URI
https://hdl.handle.net/11511/35196
Journal
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
DOI
https://doi.org/10.1007/s12215-015-0192-z
Collections
Department of Mathematics, Article
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A subgroup H of a group G is said to be a TNI-subgroup if for any Let A be an abelian group acting coprimely on the finite group G by automorphisms in such a way that for all is a solvable TNI-subgroup of G. We prove that G is a solvable group with Fitting length h(G) is at most . In particular whenever is nonnormal. Here, h(G) is the Fitting length of G and is the number of primes dividing A counted with multiplicities.
A GENERALIZED FIXED-POINT-FREE ACTION
Güloğlu, İsmail Şuayip; Ercan, Gülin (2013-05-01)
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, “Finite groups having centralizer commutator product property,”
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
, pp. 341–346, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35196.