
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)}.
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
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
| 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 |
