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Multiple Holomorphs of Finitely Generated Abelian Groups
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mills, W. H. |
| Copyright Year | 2010 |
| Abstract | The object of this paper is to determine all cases in which two or more finitely generated abelian groups have the same holomorph ('). Let G and G' be finitely generated abelian groups and let H be the holomorph of G. Then it will be shown that H is the holomorph of G' if and only if G' is an invariant maximal-abelian subgroup of H isomorphic to G. All such subgroups of H are determined. There are at most four. If G does not contain any elements of order 2, or if G has at least three independent generators of infinite order, then G itself is the only such subgroup(2). 1. Definitions. Let G be a group. If a and r are two automorphisms of G, then CTT is defined to be the automorphism such that (or)g =o,(rg) for all gGG. Under this composition the automorphisms of G form a group A. Consider the set H of all pairs (g, a), g(E.G, aG-<4. We define a composition in H by |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1951-071-03/S0002-9947-1951-0045117-2/S0002-9947-1951-0045117-2.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Maximal set Subgroup A Nepoviruses |
| Content Type | Text |
| Resource Type | Article |
