Action of a Frobenius-like group with fixed-point free kernel

Download

index.pdf

Date

2014-09-01

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

217
views

0
downloads

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 this result are also derived.

Subject Keywords

Algebra and Number Theory

URI

https://hdl.handle.net/11511/38368

Journal

JOURNAL OF GROUP THEORY

DOI

https://doi.org/10.1515/jgt-2014-0002

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Galois structure of modular forms of even weight Gurel, E. (Elsevier BV, 2009-10-01) We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Some maximal function fields and additive polynomials GARCİA, Arnaldo; Özbudak, Ferruh (Informa UK Limited, 2007-01-01) We derive explicit equations for the maximal function fields F over F-q(2n) given by F = F-q(2n) (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field F-q(2n), and where A(Y) is q- additive and deg(f) = q(n) + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over F-q(2n) (i.e., the extension H/F is Galois).
On the deformation chirality of real cubic fourfolds Finashin, Sergey (Wiley, 2009-09-01) According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
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.
Regularities in noncommutative Banach algebras Dosiev, Anar (Springer Science and Business Media LLC, 2008-07-01) In this paper we introduce regularities and subspectra in a unital noncommutative Banach algebra and prove that there is a correspondence between them similar to the commutative case. This correspondence involves a radical on a class of Banach algebras equipped with a subspectrum. Taylor and Slodkowski spectra for noncommutative tuples of bounded linear operators are the main examples of subspectra in the noncommutative case.

Citation Formats

G. Ercan, “Action of a Frobenius-like group with fixed-point free kernel,” JOURNAL OF GROUP THEORY, pp. 863–873, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38368.