Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Finite groups having centralizer commutator product property
Date
2015-12-01
Author
Ercan, Gülin
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
280
views
0
downloads
Cite This
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
Suggestions
OpenMETU
Core
On abelian group actions with TNI-centralizers
Ercan, Gülin (2019-07-03)
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.
Groups of automorphisms with TNI-centralizers
Ercan, Gülin (2018-03-15)
A subgroup H of a finite group G is called a TNI-subgroup if N-G(H) boolean AND H-9 = 1 for any g is an element of G \ N-G (H). Let A be a group acting on G by automorphisms where C-G(A) is a TNI-subgroup of G. We prove that G is solvable if and only if C-G(A) is solvable, and determine some bounds for the nilpotent length of G in terms of the nilpotent length of C-G(A) under some additional assumptions. We also study the action of a Frobenius group FH of automorphisms on a group G if the set of fixed point...
On the index of fixed point subgroup
Türkan, Erkan Murat; Ercan, Gülin; Department of Mathematics (2011)
Let G be a finite group and A be a subgroup of Aut(G). In this work, we studied the influence of the index of fixed point subgroup of A in G on the structure of G. When A is cyclic, we proved the following: (1) [G,A] is solvable if this index is squarefree and the orders of G and A are coprime. (2) G is solvable if the index of the centralizer of each x in H-G is squarefree where H denotes the semidirect product of G by A. Moreover, for an arbitrary subgroup A of Aut(G) whose order is coprime to the order o...
A generalized fixed point free automorphism of prime power order
Ercan, Gülin (2012-06-01)
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.
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.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.