Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Uniqueness theorems for global mixed groups

Uniqueness theorems for global mixed groups Abstract. An equivalence theorem is established for global Warfield groups; if G is a global Warfield group, sufficient conditions are established for two subgroups H and H' to be equivalent in the sense that an automorphism of G maps Honto H'. The equivalence theorem is then applied to obtain a uniqueness theorem for a broad class of mixed groups. 1980 Mathematics Classification (1985 Revision): 20K21; 20K27, 20K30. 1. Introduction In this paper, we establish an equivalence theorem for isotype subgroups of global Warfield groups which we then apply to the classification of certain mixed abelian groups. All groups considered herein are abelian, and we recall that an abelian group is said to be simply presented'u it can be defined by generators and relations in such a way that all the relations involve at most two generators. A Warfield group is a mixed group that is isomorphic to a direct summand of a simply presented group, and the redundant adjective "global" is traditionally affixed to contrast with the earlier devloped theory of local Warfield groups. By an equivalence theorem, we understand one that under appropriate hypotheses on subgroups H and H' of G and G', respectively, guarantees the existence http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Uniqueness theorems for global mixed groups

Hill, Paul; Megibben, Charles
Forum Mathematicum , Volume 6 (6) – Jan 1, 1994
Download PDF
14 pages

Loading next page...
 
/lp/de-gruyter/uniqueness-theorems-for-global-mixed-groups-wsdvrMahUX

References (15)

Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1994.6.139
Publisher site
See Article on Publisher Site

Abstract

Abstract. An equivalence theorem is established for global Warfield groups; if G is a global Warfield group, sufficient conditions are established for two subgroups H and H' to be equivalent in the sense that an automorphism of G maps Honto H'. The equivalence theorem is then applied to obtain a uniqueness theorem for a broad class of mixed groups. 1980 Mathematics Classification (1985 Revision): 20K21; 20K27, 20K30. 1. Introduction In this paper, we establish an equivalence theorem for isotype subgroups of global Warfield groups which we then apply to the classification of certain mixed abelian groups. All groups considered herein are abelian, and we recall that an abelian group is said to be simply presented'u it can be defined by generators and relations in such a way that all the relations involve at most two generators. A Warfield group is a mixed group that is isomorphic to a direct summand of a simply presented group, and the redundant adjective "global" is traditionally affixed to contrast with the earlier devloped theory of local Warfield groups. By an equivalence theorem, we understand one that under appropriate hypotheses on subgroups H and H' of G and G', respectively, guarantees the existence

Journal

Forum Mathematicum – de Gruyter

Published: Jan 1, 1994

There are no references for this article.