Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
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
Groups of automorphisms with TNI-centralizers
Date
2018-03-15
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
136
views
0
downloads
Cite This
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 points C-G(F) of the kernel F forms a TNI-subgroup, and obtain a bound for the nilpotent length of G in terms of the nilpotent lengths of C-G(F) and C-G(H).
Subject Keywords
TNI-subgroup
,
Automorphism
,
Centralizer
,
Frobenius group
URI
https://hdl.handle.net/11511/39221
Journal
JOURNAL OF ALGEBRA
DOI
https://doi.org/10.1016/j.jalgebra.2017.10.021
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
Finite groups having centralizer commutator product property
Ercan, Gülin (2015-12-01)
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.
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.
Rank and Order of a Finite Group Admitting a Frobenius-Like Group of Automorphisms
Ercan, Gülin; Khukhro, E. I. (2014-07-01)
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 FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a finite group G admits a Frobenius-like group of automorphisms FH of coprime order with certain additional restrictions (which are satisfied, in particular, if either |FH| is odd or |H| = 2). In the case where G is a finite p-group such that G = [G, F] it is proved that the rank of G is bounded ab...
GROUPS WHOSE PROPER SUBGROUPS HAVE RESTRICTED INFINITE CONJUGACY CLASSES
De Falco, Maria; De Giovanni, Francesco; Kuzucuoğlu, Mahmut; Musella, Carmela (2017-01-01)
A group G is said to have the AFC-property if for each element x of G at least one of the indices vertical bar G : C-G (x)vertical bar and vertical bar C-G (x) : x vertical bar is finite. The class of AFC-groups, which generalize FC-groups, has been studied by De Falco et al. (2017) and Shalev (1994). Here the structure of groups whose proper subgroups have the AFC-property is investigated.
Action of a Frobenius-like group
Güloǧlu, Ismail Ş.; Ercan, Gülin (2014-03-15)
We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F, h] = F for all nonidentity elements h is an element of H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically closed field has an H-regular direct summand if either F is fixed point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of t...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
G. Ercan, “Groups of automorphisms with TNI-centralizers,”
JOURNAL OF ALGEBRA
, pp. 38–46, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39221.