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
Implications of the index of a fixed point subgroup
Download
index.pdf
Date
2019-01-01
Author
Turkan, Erkan Murat
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
150
views
0
downloads
Cite This
Let G be a finite group and A <= Aut(G). The index vertical bar G:C-G(A)vertical bar is called the index of A in G and is denoted by Ind(G)(A). In this paper, we study the influence of Ind(G)(A) on the structure of G and prove that [G, A] is solvable in case where A is cyclic, Ind G(A) is squarefree and the orders of G and A are coprime. Moreover, for arbitrary A <= Aut(G) whose order is coprime to the order of G, we show that when [G, A] is solvable, the Fitting height of [G, A] is bounded above by the number of primes (counted with multiplicities) dividing Ind(G)(A) and this bound is best possible.
Subject Keywords
Mathematical Physics
,
Geometry and Topology
,
Algebra and Number Theory
,
Analysis
URI
https://hdl.handle.net/11511/63724
Journal
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA
DOI
https://doi.org/10.4171/rsmup/26
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
Some sufficient conditions for p-nilpotency of a finite group
Kızmaz, Muhammet Yasir (Informa UK Limited, 2019-09-02)
Let G be a finite group and let p be prime dividing . In this article, we supply some sufficient conditions for G to be p-nilpotent (see Theorem 1.2) as an extension of the main theorem of Li et al. (J. Group Theor. 20(1): 185-192, 2017).
Good action on a finite group
Ercan, Gülin; Jabara, Enrico (Elsevier BV, 2020-10-01)
Let G and A be finite groups with A acting on G by automorphisms. In this paper we introduce the concept of "good action"; namely we say the action of A on G is good, if H = [H, B]C-H (B) for every subgroup B of A and every B-invariant subgroup H of G. This definition allows us to prove a new noncoprime Hall-Higman type theorem.
ON THE NUMBER OF QUADRATIC FORMS HAVING CODIMENSION 2 RADICALS IN CHARACTERISTIC 2 GIVING MAXIMAL/MINIMAL CURVES
Özbudak, Ferruh (Informa UK Limited, 2014-09-02)
Let F-q be an arbitrary finite field of characteristic 2 and k be an arbitrary even integer. We count the number of quadratic forms having codimension 2 radicals on F-q(k) over F-q such that the corresponding curve is maximal or minimal. This problem is first attempted in [3], in which the number of maximal curves is obtained only for (q, k) = (2, 6) and (q, k) = (2, 8).
The classical involution theorem for groups of finite Morley rank
Berkman, A (Elsevier BV, 2001-09-15)
This paper gives a partial answer to the Cherlin-Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. The classification of the generic case of tame groups of odd type follows from the main result of this work, which is an analogue of Aschbacher's Classical Involution Theorem for finite simple groups. (C) 2001 Academic Press.
Invariant subspaces for banach space operators with a multiply connected spectrum
Yavuz, Onur (Springer Science and Business Media LLC, 2007-07-01)
We consider a multiply connected domain Omega = D \U (n)(j= 1) (B) over bar(lambda(j), r(j)) where D denotes the unit disk and (B) over bar(lambda(j), r(j)) subset of D denotes the closed disk centered at lambda(j) epsilon D with radius r(j) for j = 1,..., n. We show that if T is a bounded linear operator on a Banach space X whose spectrum contains delta Omega and does not contain the points lambda(1),lambda(2),...,lambda(n), and the operators T and r(j)( T -lambda I-j)(-1) are polynomially bounded, then th...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
E. M. Turkan, “Implications of the index of a fixed point subgroup,”
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA
, pp. 1–7, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63724.