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
Rank and Order of a Finite Group Admitting a Frobenius-Like Group of Automorphisms
Date
2014-07-01
Author
Ercan, Gülin
Khukhro, E. I.
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
197
views
0
downloads
Cite This
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 above in terms of |H| and the rank of the fixed-point subgroup C (G) (H), and that |G| is bounded above in terms of |H| and |C (G) (H)|. As a corollary, in the case where G is an arbitrary finite group estimates are obtained of the form |G| a parts per thousand currency sign|C (G) (F)| center dot f(|H|, |C (G) (H)|) for the order, and r(G) a parts per thousand currency sign r(C (G) (F)) + g(|H|, r(C (G) (H))) for the rank, where f and g are some functions of two variables.
Subject Keywords
Order
,
Rank
,
Frobenius group
,
Finite group
,
Automorphism
URI
https://hdl.handle.net/11511/40525
Journal
ALGEBRA AND LOGIC
DOI
https://doi.org/10.1007/s10469-014-9287-4
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
Frobenius-like groups as groups of automorphisms
Ercan, Gülin; Khukhro, Evgeny (2014-01-01)
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]. Such subgroups and sections are abundant in any nonnilpotent finite group. We discuss several recent results about the properties of a finite group G admitting a Frobenius-like group of automorphisms FH aiming at restrictions on G in terms of C-G(H) and focusing mainly on bounds for the Fitting height and rela...
The Influence of some embedding properties of subgroups on the structure of a finite group
Kızmaz, Muhammet Yasir; Ercan, Gülin; Department of Mathematics (2018)
In a finite group $G$, a subgroup $H$ is called a $TI$-subgroup if $H$ intersects trivially with distinct conjugates of itself. Suppose that $H$ is a Hall $pi$-subgroup of $G$ which is also a $TI$-subgroup. A famous theorem of Frobenius states that $G$ has a normal $pi$-complement whenever $H$ is self normalizing. In this case, $H$ is called a Frobenius complement and $G$ is said to be a Frobenius group. A first main result in this thesis is the following generalization of Frobenius' Theorem. textbf{Theorem...
Derived length of a Frobenius-like kernel
Ercan, Gülin; Khukhro, Evgeny (2014-08-15)
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F called kernel which has a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a Frobenius-like group FH acts faithfully by linear transformations on a vector space V over a field of characteristic that does not divide vertical bar FH vertical bar. It is proved that the derived length of the kernel F is bounded solely in terms of the dimension m = dim C-V(H...
Frobenius groups of automorphisms with almost fixed point free kernel
Ercan, Gülin (2019-03-01)
Let FH be a Frobenius group with kernel F and complement H, acting coprimely on the finite solvable group G by automorphisms. We prove that if C-G(H) is of Fitting length n then the index of the n-th Fitting subgroup F-n(G) in G is bounded in terms of vertical bar C-G(F)vertical bar and vertical bar F vertical bar. This generalizes a result of Khukhro and Makarenko [6] which handles the case n = 1.
Prime graphs of solvable groups
Ulvi , Muhammed İkbal; Ercan, Gülin; Department of Electrical and Electronics Engineering (2020-8)
If $G$ is a finite group, its prime graph $Gamma_G$ is constructed as follows: the vertices are the primes dividing the order of $G$, two vertices $p$ and $q$ are joined by an edge if and only if $G$ contains an element of order $pq$. This thesis is mainly a survey that gives some important results on the prime graphs of solvable groups by presenting their proofs in full detail.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
G. Ercan and E. I. Khukhro, “Rank and Order of a Finite Group Admitting a Frobenius-Like Group of Automorphisms,”
ALGEBRA AND LOGIC
, pp. 258–265, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40525.