Units and augmentation powers in integral group rings-Reference-Cited by-同舟云学术

Units and augmentation powers in integral group rings

Published:2020-07-16 Issue:6 Volume:23 Page:931-944
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Maheshwary Sugandha¹,Passi Inder Bir S.²

Affiliation:

1. Indian Institute of Science Education and Research , Mohali, Sector 81 , Mohali (Punjab)-140306 , India

2. Centre for Advanced Study in Mathematics , Panjab University , Chandigarh -160014 ; and Indian Institute of Science Education and Research, Mohali, Sector 81, Mohali (Punjab)-140306 , India

Abstract

Abstract The augmentation powers in an integral group ring ℤ ⁢ G

{\mathbb{Z}G}

induce a natural filtration of the unit group of ℤ ⁢ G

{\mathbb{Z}G}

analogous to the filtration of the group G given by its dimension series { D n ⁢ ( G ) } n ≥ 1

{\{D_{n}(G)\}_{n\geq 1}}

. The purpose of the present article is to investigate this filtration, in particular, the triviality of its intersection.

Funder

Department of Science and Technology, Ministry of Science and Technology, India

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference16 articles.

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2. A. Bächle, M. Caicedo, E. Jespers and S. Maheshwary, Global and local properties of finite groups with only finitely many central units in their integral group ring, preprint (2018), https://arxiv.org/abs/1808.03546v2.

3. G. K. Bakshi, S. Maheshwary and I. B. S. Passi, Integral group rings with all central units trivial, J. Pure Appl. Algebra 221 (2017), no. 8, 1955–1965.

4. G. K. Bakshi, S. Maheshwary and I. B. S. Passi, Group rings and the RS property, Comm. Algebra 47 (2019), no. 3, 969–977.

5. N. Gupta, Free Group Rings, Contemp. Math. 66, American Mathematical Society, Providence, 1987.

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