On abelian group actions with TNI-centralizers

Download

index.pdf

Date

2019-07-03

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

275
views

0
downloads

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.

Subject Keywords

Automorphism, Centralizer, Fitting length, TNI-subgroup

URI

https://hdl.handle.net/11511/39720

Journal

COMMUNICATIONS IN ALGEBRA

DOI

https://doi.org/10.1080/00927872.2018.1549662

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.
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.
Locally finite groups and their subgroups with small centralizers ERSOY, KIVANÇ; Kuzucuoğlu, Mahmut; Shunwatsky, Pavel (2017-07-01) Let p be a prime and G a locally finite group containing an elementary abelian p-subgroup A of rank at least 3 such that C-G(A) is Chernikov and C-G(a) involves no infinite simple groups for any a is an element of A(#). We show that G is almost locally soluble (Theorem 1.1). The key step in the proof is the following characterization of PSLp(k): An infinite simple locally finite group G admits an elementary abelian p-group of automorphisms A such that C-G(A) is Chernikov and C-G(A) Keywords: involves no inf...
On algebraic function fields with class number three Buyruk, Dilek; Bilhan, Mehpare; Özbudak, Ferruh; Department of Mathematics (2011) Let K/Fq be an algebraic function field with full constant field Fq and genus g. Then the divisor class number hK of K/Fq is the order of the quotient group, D0K /P(K), degree zero divisors of K over principal divisors of K. The classification of the function fields K with hK = 1 is done by MacRea, Leitzel, Madan and Queen and the classification of the extensions with class number two is done by Le Brigand. Determination of the necessary and the sufficient conditions for a function field to have class numbe...
Inequalities for harmonic functions on spheroids and their applications Zahariuta, V (2001-06-01) Hadamard-type interpolational inequalities for norms of harmonic functions are studied for confocal prolate and oblate spheroids. It is shown that the optimal level domains in such inequalities may be non-spheroidal. Moreover, in contrary with the case of analytic functions, there is an unremovable gap between the corresponding optimal level domains for inner and outer versions of Hadamard-type inequalities for harmonic functions. These results are based on some special asymptotical formulas for associated ...

Citation Formats

G. Ercan, “On abelian group actions with TNI-centralizers,” COMMUNICATIONS IN ALGEBRA, pp. 3003–3006, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39720.