Normalizers of finite subgroups in homogenous symmetric groups and automorphisms

Date

2019-05-21

Author

Guven, Ulviye Bursra
Kuzucuoğlu, Mahmut

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

267
views

0
downloads

The structure of the centralizers of finite subgroups in homogenous symmetric groups S(chi(xi)) are given up to isomorphism by Guven-Kegel-Kuzucuoglu in 2015 and Kuzucuoglu-Oliynyk-Sushchansky in 2018. In this article, we answer the natural question; what is the structure of the normalizers of finite semiregular subgroups in homogenous symmetric groups? We prove, N-S(chi(xi))(F) congruent to C-S(chi(xi) (F) x Aut(F) congruent to Sigma(chi(xi 1))(F) x Aut(F) for some sequence xi(1): We answer negatively, the following open question: does every automorphism of S(chi(xi)) preserve a level? We show that, there exist uncountably many automorphisms of S(chi(xi)) which does not preserve any level. Finally, we show that the level preserving automorphisms of the homogenous finitary symmetric group FSym(kappa)(chi(xi)) is isomorphic to Sym(kappa) x Pi(i is an element of N) CSym(kappa)(mi+1) (FSym(kappa)(m(i))).

Subject Keywords

Algebra and Number Theory

URI

https://hdl.handle.net/11511/34578

Journal

COMMUNICATIONS IN ALGEBRA

DOI

https://doi.org/10.1080/00927872.2019.1612423

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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.
Centralizers of involutions in locally finite groups Kuzucuoğlu, Mahmut (Informa UK Limited, 2007-01-01) The present article deals with locally finite groups G having an involution phi such that C-G(phi) is an SF-group. It is shown that G possesses a normal subgroup B which is a central product of. nitely many groups isomorphic to PSL(2, K-i) or SL(2, Ki) for some in finite locally finite fields K-i of odd characteristic, such that [G, phi]'/B and G/[G, phi] are both SF-groups.
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.
The class of (1,3)-groups with homocyclic regulator quotient of exponent p(4) has bounded representation type Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (Elsevier BV, 2014-02-15) The class of almost completely decomposable groups with a critical typeset of type (1,3) and a homocyclic regulator quotient of exponent p(4) is shown to be of bounded representation type. There are only nine near-isomorphism types of indecomposables, all of rank <= 6.
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.

Citation Formats

U. B. Guven and M. Kuzucuoğlu, “Normalizers of finite subgroups in homogenous symmetric groups and automorphisms,” COMMUNICATIONS IN ALGEBRA, pp. 5182–5191, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34578.