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A homological characterization of large subgroups

A homological characterization of large subgroups Acta Mathematica Academiae Scientiarum Hungaricae Tomus 25 (3~4), (J974), pp. 255--262. A HOMOLOGICAL CHARACTERIZATION OF LARGE SUBGROUPS By J. WINTHROP* (Columbia--Davis) 1. Introduction A large subgroup of a p-primary abelian group must, together with any basic subgroup, generate the group. This fruitful idea, originated by R. S. PmRCE (see [8]), for the purpose of "getting a handle" on the homomorphism groups of primary groups, has resulted in some very beautiful discoveries. We mention here only the remarkable theorem of CUTLER and STRINGALL [3] that the completion with respect to the topology generated by the large subgroups is precisely the torsion completion with respect to the p-adic topology. For other interesting work on large subgroups see MEGIBBEN [6], and especially the recent paper of BENABDALLAH, EISENSTADT, IRWIN, and POLUIANOV [1]. Our initial sentence above serves to define the notion of a large subgroup only if we further demand that a large subgroup be fully invariant, and it is this aspect which we wish to investigate below. In particular we will show that all large subgroups may be described as functorial subgroups, i.e. as preradicals in the sense of NUNKE [7]. Our motivation in this work is to provide a way http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Academiae Scientiarum Hungarica Springer Journals

A homological characterization of large subgroups

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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general
ISSN
0001-5954
eISSN
1588-2632
DOI
10.1007/BF01886082
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Abstract

Acta Mathematica Academiae Scientiarum Hungaricae Tomus 25 (3~4), (J974), pp. 255--262. A HOMOLOGICAL CHARACTERIZATION OF LARGE SUBGROUPS By J. WINTHROP* (Columbia--Davis) 1. Introduction A large subgroup of a p-primary abelian group must, together with any basic subgroup, generate the group. This fruitful idea, originated by R. S. PmRCE (see [8]), for the purpose of "getting a handle" on the homomorphism groups of primary groups, has resulted in some very beautiful discoveries. We mention here only the remarkable theorem of CUTLER and STRINGALL [3] that the completion with respect to the topology generated by the large subgroups is precisely the torsion completion with respect to the p-adic topology. For other interesting work on large subgroups see MEGIBBEN [6], and especially the recent paper of BENABDALLAH, EISENSTADT, IRWIN, and POLUIANOV [1]. Our initial sentence above serves to define the notion of a large subgroup only if we further demand that a large subgroup be fully invariant, and it is this aspect which we wish to investigate below. In particular we will show that all large subgroups may be described as functorial subgroups, i.e. as preradicals in the sense of NUNKE [7]. Our motivation in this work is to provide a way

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Acta Mathematica Academiae Scientiarum Hungarica – Springer Journals

Published: Sep 1, 1974

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