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Unitary and Symmetric Units of a Commutative Group Algebra

Part of: Representation theory of groups Rings and algebras arising under various constructions Conditions on elements

Published online by Cambridge University Press:  27 December 2018

V. A. Bovdi  and
A. N. Grishkov
V. A. Bovdi*
Affiliation:
UAEU, Al-Ain, United Arab Emirates (vbovdi@gmail.com)
A. N. Grishkov
Affiliation:
IME USP, Citade Universitària, Sao Paulo, Brazil (shuragri@gmail.com) and Omsk F.M. Dostoevsky State University, Omsk Russia
*
*Corresponding author.
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Abstract

Let F be a field of characteristic two and G a finite abelian 2-group with an involutory automorphism η. If G = H × D with non-trivial subgroups H and D of G such that η inverts the elements of H (H without a direct factor of order 2) and fixes D element-wise, then the linear extension of η to the group algebra FG is called a nice involution. This determines the groups of unitary and symmetric normalized units of FG. We calculate the orders and the invariants of these subgroups.

Keywords

group ringunitary groupsymmetric elementcommutative ringinvolution

MSC classification

Primary: 16S34: Group rings , Laurent polynomial rings 16U60: Units, groups of units
Secondary: 20C05: Group rings of finite groups and their modules
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 641 - 654
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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