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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2017: 0.67

Online
ISSN
1435-5337
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Volume 27, Issue 5

Issues

Subgroups which admit extensions of homomorphisms

Simion Breaz
  • Faculty of Mathematics and Computer Science, “Babeş-Bolyai” University, Str. Mihail Kogălniceanu 1, 400084 Cluj-Napoca, Romania
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/ Grigore Călugăreanu
  • Faculty of Mathematics and Computer Science, “Babeş-Bolyai” University, Str. Mihail Kogălniceanu 1, 400084 Cluj-Napoca, Romania
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/ Phill Schultz
Published Online: 2013-09-12 | DOI: https://doi.org/10.1515/forum-2013-0089

Abstract

We classify by numerical invariants the finite subgroups H of a primary abelian group G for which every homomorphism or monomorphism of H into G, or every endomorphism of H, extends to an endomorphism of G. We apply these results to show that for finitely generated subgroups of general abelian groups, the extendibility of monomorphisms implies the extendibility of all homomorphisms.

Keywords: Abelian group; extending homomorphisms; Ulm sequence; valuation

MSC: 20K30; 20K10; 16D50

About the article

Received: 2013-05-30

Published Online: 2013-09-12

Published in Print: 2015-09-01


Funding Source: CNCS-UEFISCDI

Award identifier / Grant number: PN-II-RU-TE-2011-3-0065


Citation Information: Forum Mathematicum, Volume 27, Issue 5, Pages 2533–2549, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2013-0089.

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