Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Illinois Journal of ...arrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
Illinois Journal of Mathematics
Article
License: implied-oa
Data sources: UnpayWall
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
Project Euclid
Other literature type . 1977
Data sources: Project Euclid
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Archiv der Mathematik
Article . 1977 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article
Data sources: zbMATH Open
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1977
Data sources: zbMATH Open
Illinois Journal of Mathematics
Article . 1977 . Peer-reviewed
Data sources: Crossref
versions View all 5 versions
addClaim

On the automorphism group of an integral group ring, I

On the automorphism group of an integral group ring. II
Authors: Peterson, Gary L.;

On the automorphism group of an integral group ring, I

Abstract

Let G be a finite group, Z(G) denote the integral group ring ofG, and NA(G) denote the group of normalized automorphisms of Z(G). That is, NA(G) denotes the group of ring automorphismsfof Z(G) such thatf(g) has augmentation one for all g e G. As remarked in [1] and [5], little generality is lost by studying normalized automorphisms over arbitrary automorphisms of Z(G). The objective of this paper is to extend the previously known list of metabelian E. R. groups. E. R. groups are groups G in which every element ofNA(G) has an elementary representation. Here, by saying that f in NA(G) has an elementary representation, we mean that f can be written in the form f where tr lies in the automorphism group of G, denoted by Aut (G), (actually extended linearly to Z(G)) and zu denotes conjugation by a unit u in Q(G) (the group algebra ofG over the rational field). In the notation of[5], saying that G is an E. R. group is equivalent to saying that NA(G)= CP(G) Aut (G) where CP(G) {zlu is a unit in Q(G)normalizing Z(G)}.

Keywords

Group rings, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, 16A26, Group rings of finite groups and their modules (group-theoretic aspects), Automorphisms of abstract finite groups, Automorphisms and endomorphisms

  • BIP!
    Impact byBIP!
    citations
    The total number of citations received by all articles of the researcher of interest.
    10
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
citations
The total number of citations received by all articles of the researcher of interest.
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Average
Top 10%
Average
Green
hybrid