The upper central series of the maximal normal 𝑝-subgroup of a group of automorphisms-Reference-Cited by-同舟云学术

The upper central series of the maximal normal 𝑝-subgroup of a group of automorphisms

Published:2021-03-06 Issue:6 Volume:24 Page:1213-1244
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Aviño Maria Alicia¹,Schultz Phill²,Zyman Marcos³

Affiliation:

1. Department of Mathematics , Instituto Tecnológico de Estudios Superiores Monterrey , Calle del Puente 222, Col. Ejidos de Huipulco, 14380 , Mexico City , Mexico

2. Department of Mathematics , University of Western Australia , 35 Stirling Highway, 6009 , Perth , Australia

3. Department of Mathematics , The City University of New York-BMCC , 199 Chambers Street , New York , NY 10007 , USA

Abstract

Abstract Let 𝐺 be a bounded abelian 𝑝-group, with automorphism group Aut ⁡ ( G )

\operatorname{Aut}(G)

. Whenever 𝐺 satisfies certain conditions, we determine the upper central series and nilpotency class of the maximal normal 𝑝-subgroup of Aut ⁡ ( G )

\operatorname{Aut}(G)

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2020-0106/pdf

Reference17 articles.

1. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Grad. Texts in Math. 13, Springer, New York, 1974,

2. M. A. Aviñó, On the automorphism group of a finite abelian 𝑝-group, preprint (1996), Institute of Mathematics UNAM, 479, 1–22.

3. M. A. Aviñó, Splitting the automorphism group of an abelian 𝑝-group, Bol. Soc. Mat. Mex. (3) 6 (2000), no. 2, 171–175.

4. M. A. Aviñó and P. Schultz, The endomorphism ring of a bounded abelian 𝑝-group, Abelian Groups, Rings and Modules (Perth 2000), Contemp. Math. 273, American Mathematical Society, Providence (2001), 75–84.

5. A. E. Clement, S. Majewicz and M. Zyman, The Theory of Nilpotent Groups, Birkhäuser/Springer, Cham, 2017.